Pith Number

pith:4AZWASTA

pith:2026:4AZWASTAB4PGNFKDCMPSWCNNXB

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The dual of the Hardy space associated to the Dunkl-Schr\"odinger operator with reverse H\"older class potential

P. Athulya, S.K. Verma

The dual of the Hardy space H^1 for the Dunkl-Schrödinger operator is the space BMO(L_k)

arxiv:2605.14456 v1 · 2026-05-14 · math.FA

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\pithnumber{4AZWASTAB4PGNFKDCMPSWCNNXB}

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Record completeness

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3 Author claim open · sign in to claim

4 Citations open

5 Replications open

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

The dual space of H_{tilde L_k}^1 is BMO(L_k), a subspace of the Dunkl BMO_k space, characterized via atomic decomposition where the cancellation condition of atoms depends on the critical radius function associated with V.

C2weakest assumption

The potential V belongs to the reverse Hölder class RH_k^q(R^n) with q > max{1, (n+2γ)/2}, which is required for the atomic decomposition and the definition of the critical radius function to work as stated.

C3one line summary

The dual of the Hardy space H^1 for the Dunkl-Schrödinger operator L_k is the BMO(L_k) space, characterized via atoms whose cancellation depends on the critical radius function of the reverse Hölder potential V.

References

39 extracted · 39 resolved · 1 Pith anchors

[1] D. Aalto, L. Berkovits, O.E. Kansanen, H. Yue, John-Nirenberg lemmas for a doubling measure. Studia Math.204(1):21-37 (2011) 2011

[2] V.Almeida, J.J. Betancor, J.C. Fari˜ na, L. Rodr´ ıguez-Mesa, Maximal, Littlewood-Paley, Varia- tion, and oscillation operators in the Dunkl setting. J. Fourier Anal. Appl.30(5):60(1-41) (2024) 2024

[3] B. Amri, A. Hammi, Dunkl-Schr¨ odinger operators. Complex Anal. Oper. Theory.13(3):1033- 1058 (2019) 2019

[4] B. Amri, A. Hammi, Semigroup and Reisz transform for the Dunkl-Schr¨ odinger operators. Semi- group Forum.101(3):507-533 (2020) 2020

[5] J.P. Anker, J. Dziuba´ nski, A. Hejna, Harmonic functions, conjugate harmonic functions and the Hardy spaceH 1 in the rational Dunkl setting. J. Fourier Anal. Appl.25(5):2356-2418 (2019) 2019

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-17T23:39:06.836304Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e033604a600f1e669543131f2b09adb86c2af1c9561c3d3690b25275dd5a02c4

Aliases

arxiv: 2605.14456 · arxiv_version: 2605.14456v1 · doi: 10.48550/arxiv.2605.14456 · pith_short_12: 4AZWASTAB4PG · pith_short_16: 4AZWASTAB4PGNFKD · pith_short_8: 4AZWASTA

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/4AZWASTAB4PGNFKDCMPSWCNNXB \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: e033604a600f1e669543131f2b09adb86c2af1c9561c3d3690b25275dd5a02c4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1ec3e0af0118ad4c2b06f7b57b3d4c695e41c125e99867ab2c47c615750262da",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2026-05-14T06:51:22Z",
    "title_canon_sha256": "6e9c835c68cbcc9e0816ccaa9cd177f70f9d4ff2360b8fe33b1b36474cfa894c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.14456",
    "kind": "arxiv",
    "version": 1
  }
}