Paper Citation Record · LEDGER

The conformal logarithmic Laplacian on the sphere: Yamabe-type problems and Sobolev spaces

As of 8 August 2026, this Paper Citation Record lists 40 of 40 outbound references and 4 inbound Pith citation observations for arXiv:2507.21779.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2507.21779 v2

Coverage vector

measured 40 of 40 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T12:34:41.716120Z

measured 44 of 44 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-08T06:32:00.761636+00:00

measured 4 of 4 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-06-28T07:11:55.856137Z

measured 1 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: arxiv_reference, observed 2026-08-05T02:28:24.338817Z

Reference resolution

40 of 40 outbound references displayed

verified exact3
verified fuzzy22
unresolved15
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

0
arxiv_reference, observed 2026-08-05T02:28:24.338817Z

Outbound references

Observation 3ef84960-366d-47a6-96b1-db526d629a39 · outbound

This paper cites Alzer, On some inequalities for the gamma and psi functions , Mathematics of computations, 66 (1997), pp.

The conformal logarithmic Laplacian on the sphere: Yamabe-type problems and Sobolev spaces Alzer, On some inequalities for the gamma and psi functions , Mathematics of computations, 66 (1997), pp

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:34:42.986643Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation c379b1c0-7631-4e50-b6fa-32a094952025 · outbound

This paper cites Angeles and A.

The conformal logarithmic Laplacian on the sphere: Yamabe-type problems and Sobolev spaces Angeles and A

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:34:42.954572Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation eb8583f6-172c-434a-aeba-e401cf2f0d8b · outbound

This paper cites Arora, J.

The conformal logarithmic Laplacian on the sphere: Yamabe-type problems and Sobolev spaces Arora, J

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-06T12:34:41.502211Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fe4a7588-3f4b-42d7-98b2-48193b7ff0eb · outbound

This paper cites Beckner, Sobolev inequalities, the Poisson semigroup, and analysis on the sphere sn., Proceedings of the National Academy of Sciences, 89 (1992), pp.

The conformal logarithmic Laplacian on the sphere: Yamabe-type problems and Sobolev spaces Beckner, Sobolev inequalities, the Poisson semigroup, and analysis on the sphere sn., Proceedings of the National Academy of Sciences, 89 (1992), pp

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:34:42.920366Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 69385304-85de-4f07-b8cc-9d809f1d8525 · outbound

This paper cites 1897–1905.

The conformal logarithmic Laplacian on the sphere: Yamabe-type problems and Sobolev spaces 1897–1905

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:34:42.892067Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 55103a0a-cfdf-4e81-a3ed-39916b267f77 · outbound

This paper cites an unresolved cited work.

The conformal logarithmic Laplacian on the sphere: Yamabe-type problems and Sobolev spaces Unresolved cited work

Reference 6

Resolution: unresolved; raw_fallback, observed 2026-08-06T12:34:42.860650Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation b997d600-d672-4c1d-9af2-d8b641c1c1d9 · outbound

This paper cites Brasco, D.

The conformal logarithmic Laplacian on the sphere: Yamabe-type problems and Sobolev spaces Brasco, D

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:34:42.833222Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation c3015175-03f8-4d2c-8b7a-c4e645b9682d · outbound

This paper cites an unresolved cited work.

The conformal logarithmic Laplacian on the sphere: Yamabe-type problems and Sobolev spaces Unresolved cited work

Reference 8

Resolution: unresolved; raw_fallback, observed 2026-08-06T12:34:42.804727Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation f25f4e8a-eb6a-453b-be57-dd1b034bb163 · outbound

This paper cites Fractional $Q$-curvature on the sphere and optimal partitions.

The conformal logarithmic Laplacian on the sphere: Yamabe-type problems and Sobolev spaces Fractional $Q$-curvature on the sphere and optimal partitions

Reference 9

Resolution: verified exact; local_arxiv, observed 2026-08-06T12:34:41.913019Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation e16fc599-1233-406f-9b5e-29eca6343764 · outbound

This paper cites an unresolved cited work.

The conformal logarithmic Laplacian on the sphere: Yamabe-type problems and Sobolev spaces Unresolved cited work

Reference 10

Resolution: unresolved; raw_fallback, observed 2026-08-06T12:34:42.775434Z

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No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 31dd888a-b8d3-4986-a4db-15f4c45c7ed2 · outbound

This paper cites Chen, On m-order logarithmic Laplacians and the applications , Analysis and Applications, (2025), pp.

The conformal logarithmic Laplacian on the sphere: Yamabe-type problems and Sobolev spaces Chen, On m-order logarithmic Laplacians and the applications , Analysis and Applications, (2025), pp

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:34:42.748583Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 27008a04-9a08-42d3-bac2-d425dac2b9d8 · outbound

This paper cites An extension problem for the logarithmic Laplacian.

The conformal logarithmic Laplacian on the sphere: Yamabe-type problems and Sobolev spaces An extension problem for the logarithmic Laplacian

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-06T12:34:41.571078Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 100acb69-947b-4fd5-a4b7-1ac33e68c636 · outbound

This paper cites Chen and L.

The conformal logarithmic Laplacian on the sphere: Yamabe-type problems and Sobolev spaces Chen and L

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:34:42.726687Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation d7c5d3f6-877b-44b1-8e24-a0fd22b713ed · outbound

This paper cites an unresolved cited work.

The conformal logarithmic Laplacian on the sphere: Yamabe-type problems and Sobolev spaces Unresolved cited work

Reference 14

Resolution: unresolved; raw_fallback, observed 2026-08-06T12:34:42.705551Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation f761246e-e05d-473c-b4a9-e52367397d4b · outbound

This paper cites Chen and T.

The conformal logarithmic Laplacian on the sphere: Yamabe-type problems and Sobolev spaces Chen and T

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:34:42.687151Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 9b7be800-210f-4cf4-af0a-79a6d07221f5 · outbound

This paper cites On positive solutions of critical semilinear equations involving the Logarithmic Laplacian.

The conformal logarithmic Laplacian on the sphere: Yamabe-type problems and Sobolev spaces On positive solutions of critical semilinear equations involving the Logarithmic Laplacian

Reference 16

Resolution: verified exact; local_arxiv, observed 2026-08-06T12:34:41.852088Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation e9f4d6b1-58d5-45bb-aadd-5e7e1be6d770 · outbound

This paper cites Logarithmic Laplacian on General Riemannian Manifolds.

The conformal logarithmic Laplacian on the sphere: Yamabe-type problems and Sobolev spaces Logarithmic Laplacian on General Riemannian Manifolds

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-06T12:34:41.604371Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1a884bc1-d827-4013-aa1a-a1b660e4eb3b · outbound

This paper cites Clapp, J.

The conformal logarithmic Laplacian on the sphere: Yamabe-type problems and Sobolev spaces Clapp, J

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:34:42.665320Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation d6fd6dda-068f-46d9-86c7-ccc7646cd59c · outbound

This paper cites Clapp, A.

The conformal logarithmic Laplacian on the sphere: Yamabe-type problems and Sobolev spaces Clapp, A

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:34:42.643795Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation b3f6a533-52d8-445b-91e0-6adc495bf692 · outbound

This paper cites Correa and A.

The conformal logarithmic Laplacian on the sphere: Yamabe-type problems and Sobolev spaces Correa and A

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:34:42.620355Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 76401c3b-8acd-40e1-b224-3bcb92195a08 · outbound

This paper cites del Mar Gonz ´alez, Recent Progress on the Fractional Laplacian in Conformal Geometry , De Gruyter Open Poland, Warsaw, Poland, 2017, pp.

The conformal logarithmic Laplacian on the sphere: Yamabe-type problems and Sobolev spaces del Mar Gonz ´alez, Recent Progress on the Fractional Laplacian in Conformal Geometry , De Gruyter Open Poland, Warsaw, Poland, 2017, pp

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:34:42.584991Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 03d4ae3c-510b-420a-943a-cd28b41a45d3 · outbound

This paper cites The Dirichlet Problem For the Logarithmic p-Laplacian.

The conformal logarithmic Laplacian on the sphere: Yamabe-type problems and Sobolev spaces The Dirichlet Problem For the Logarithmic p-Laplacian

Reference 22

Resolution: verified exact; local_arxiv, observed 2026-08-06T12:34:41.777023Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation b578af5b-fa0c-430b-8ac2-170c4a2d7d3c · outbound

This paper cites an unresolved cited work.

The conformal logarithmic Laplacian on the sphere: Yamabe-type problems and Sobolev spaces Unresolved cited work

Reference 23

Resolution: unresolved; raw_fallback, observed 2026-08-06T12:34:42.551715Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 418b7d24-4b3d-478b-b825-298197af6d70 · outbound

This paper cites an unresolved cited work.

The conformal logarithmic Laplacian on the sphere: Yamabe-type problems and Sobolev spaces Unresolved cited work

Reference 24

Resolution: unresolved; raw_fallback, observed 2026-08-06T12:34:42.520827Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 7bcbb825-5b19-471b-9fa2-e94d52a9e08e · outbound

This paper cites Frank, E.

The conformal logarithmic Laplacian on the sphere: Yamabe-type problems and Sobolev spaces Frank, E

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:34:42.499573Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 75f877a0-1ae0-4f2e-a665-3f21d4def557 · outbound

This paper cites an unresolved cited work.

The conformal logarithmic Laplacian on the sphere: Yamabe-type problems and Sobolev spaces Unresolved cited work

Reference 26

Resolution: unresolved; raw_fallback, observed 2026-08-06T12:34:42.470502Z

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No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 64289dac-7b2c-43fd-a2ea-a4883175f152 · outbound

This paper cites an unresolved cited work.

The conformal logarithmic Laplacian on the sphere: Yamabe-type problems and Sobolev spaces Unresolved cited work

Reference 27

Resolution: unresolved; raw_fallback, observed 2026-08-06T12:34:42.449234Z

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No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 5e86249b-b278-42b9-b1fd-915d00d585ca · outbound

This paper cites an unresolved cited work.

The conformal logarithmic Laplacian on the sphere: Yamabe-type problems and Sobolev spaces Unresolved cited work

Reference 28

Resolution: unresolved; raw_fallback, observed 2026-08-06T12:34:42.422235Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 4b4e27e0-7208-4314-9611-c4b71af732f4 · outbound

This paper cites an unresolved cited work.

The conformal logarithmic Laplacian on the sphere: Yamabe-type problems and Sobolev spaces Unresolved cited work

Reference 29

Resolution: unresolved; raw_fallback, observed 2026-08-06T12:34:42.398725Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation ef3d5de2-1258-488a-bdad-79604310a7eb · outbound

This paper cites an unresolved cited work.

The conformal logarithmic Laplacian on the sphere: Yamabe-type problems and Sobolev spaces Unresolved cited work

Reference 30

Resolution: unresolved; raw_fallback, observed 2026-08-06T12:34:42.378850Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 40d6cb66-3d1b-426f-a7d8-b04cbb06b78f · outbound

This paper cites Hern ´andez-Santamar´ıa, S.

The conformal logarithmic Laplacian on the sphere: Yamabe-type problems and Sobolev spaces Hern ´andez-Santamar´ıa, S

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:34:42.334485Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 2a957991-19ec-498e-b156-c5b582ce854d · outbound

This paper cites Hern ´andez-Santamar´ıa, L.

The conformal logarithmic Laplacian on the sphere: Yamabe-type problems and Sobolev spaces Hern ´andez-Santamar´ıa, L

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:34:42.304212Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation e1b2caf7-ebb9-4076-bb53-d0f077d6b145 · outbound

This paper cites Hern´andez Santamar´ıa and A.

The conformal logarithmic Laplacian on the sphere: Yamabe-type problems and Sobolev spaces Hern´andez Santamar´ıa and A

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:34:42.271993Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 900f7a42-e31d-4dcf-a86e-4a510de7fa54 · outbound

This paper cites Jarohs, A.

The conformal logarithmic Laplacian on the sphere: Yamabe-type problems and Sobolev spaces Jarohs, A

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:34:42.249132Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation de19a7d1-db1f-4eeb-9542-1b9d0a5bb51f · outbound

This paper cites Jarohs, A.

The conformal logarithmic Laplacian on the sphere: Yamabe-type problems and Sobolev spaces Jarohs, A

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:34:42.222504Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation e6934e31-bd47-4c31-b55a-cb8d05b76736 · outbound

This paper cites Laptev and T.

The conformal logarithmic Laplacian on the sphere: Yamabe-type problems and Sobolev spaces Laptev and T

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:34:42.192865Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation a23a29a2-aad4-404e-a1d9-39650004fb6c · outbound

This paper cites Pollastro and N.

The conformal logarithmic Laplacian on the sphere: Yamabe-type problems and Sobolev spaces Pollastro and N

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:34:42.172314Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 9762d917-7959-4f08-82ad-a2bebb323052 · outbound

This paper cites an unresolved cited work.

The conformal logarithmic Laplacian on the sphere: Yamabe-type problems and Sobolev spaces Unresolved cited work

Reference 38

Resolution: unresolved; raw_fallback, observed 2026-08-06T12:34:42.139075Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation cdda28a0-c2c2-4b1e-8f30-7bfcb4ecdd3e · outbound

This paper cites Weiyue, On a conformally invariant elliptic equation on Rn, Commun.

The conformal logarithmic Laplacian on the sphere: Yamabe-type problems and Sobolev spaces Weiyue, On a conformally invariant elliptic equation on Rn, Commun

Reference 39

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:34:42.110529Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation c5e9e3cf-c294-4b2e-90bc-6ec5044e3333 · outbound

This paper cites Yafaev, Sharp constants in the Hardy–Rellich inequalities , Journal of Functional Analysis, 168 (1999), pp.

The conformal logarithmic Laplacian on the sphere: Yamabe-type problems and Sobolev spaces Yafaev, Sharp constants in the Hardy–Rellich inequalities , Journal of Functional Analysis, 168 (1999), pp

Reference 40

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:34:42.088067Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Pith citing papers

Observation 43345ffc-f0c7-416f-8ec6-ae0115c32de6 · inbound

The Fractional-Logarithmic Laplacian:Fundamental Properties and Eigenvalues cites this paper.

The Fractional-Logarithmic Laplacian:Fundamental Properties and Eigenvalues The conformal logarithmic Laplacian on the sphere: Yamabe-type problems and Sobolev spaces

Reference 17

Resolution: verified exact; arxiv_id, observed 2026-05-16T07:02:28.909877Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 7ec65f8c-0ede-4d24-a061-f5eb08b98fad · inbound

$s$-harmonic functions in the small order limit cites this paper.

$s$-harmonic functions in the small order limit The conformal logarithmic Laplacian on the sphere: Yamabe-type problems and Sobolev spaces

Reference 17

Resolution: verified exact; arxiv_id, observed 2026-05-08T22:59:24.028044Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 338891bd-8f8e-4fc0-b381-629420b156f8 · inbound

Spectral Properties of the Logarithmic Laplacian with Indefinite Weights cites this paper.

Spectral Properties of the Logarithmic Laplacian with Indefinite Weights The conformal logarithmic Laplacian on the sphere: Yamabe-type problems and Sobolev spaces

Reference 27

Resolution: verified exact; arxiv_id, observed 2026-05-14T18:07:33.719326Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation fa4cc0eb-1cab-45c3-98c0-63b640891dcc · inbound

On the fundamental solutions of two nonlocal parabolic equations related to logarithmic Laplacians cites this paper.

On the fundamental solutions of two nonlocal parabolic equations related to logarithmic Laplacians The conformal logarithmic Laplacian on the sphere: Yamabe-type problems and Sobolev spaces

Reference 7

Resolution: verified exact; arxiv_id, observed 2026-07-02T07:06:44.084968Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.