Pith Number

pith:5ENWIYEV

pith:2026:5ENWIYEVMJBHYKJ5CBKOT3IP5D

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Hardy spaces and quasiregular mappings: averaged derivatives and the $\mathbb{BMO}$ case

Iv\'an Caama\~no, Tomasz Adamowicz

Averaged derivatives characterize the Hardy spaces H^p of quasiregular mappings with finite multiplicity on the unit ball.

arxiv:2605.13655 v1 · 2026-05-13 · math.CV · math.FA

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Claims

C1strongest claim

The averaged derivatives are employed to study the non-tangential limit functions and non-tangential maximal functions of quasiregular mappings and to characterize H^p in the case of finite multiplicity of f. Moreover, we study relations between quasiregular mappings, averaged derivatives, BMO spaces and Carleson measures on B^n and the role of the multiplicity of a map.

C2weakest assumption

The quasiregular mappings satisfy the appropriate growth and multiplicity conditions required for the Harnack estimates and characterizations to hold.

C3one line summary

Averaged derivatives characterize Hardy spaces H^p for quasiregular mappings of finite multiplicity and relate them to BMO spaces and Carleson measures on the ball.

References

16 extracted · 16 resolved · 0 Pith anchors

[1] [AF] T. Adamowicz, K. Fässler,Hardy spaces and quasiconformal maps in the Heisenberg group, J. Funct. Anal. 284 (2023), no. 6, Paper No. 109832. [AFW] T. Adamowicz, K. Fässler, B. Warhurst,A Koebe dis 2023

[2] [AG2] T. Adamowicz, M. J. González.Hardy spaces and quasiregular mappings, Trans. Amer. Math. Soc. 378 (2025), no. 9, 6265–6290. [AGG] T. Adamowicz, M. J. Gonzàlez, M. Gryszówka,ϵ-Approximability and 2025

[3] [Äk] T. Äkkinen,Radial limits of mappings of bounded and finite distortion, J. Geom. Anal. 24 (2014), no. 3, 1298–1322. [Al1] G. Alessandrini,An identification problem for an elliptic equation in two 2014

[4] [AK] K. Astala, P . Koskela,H p-theory for Quasiconformal Mappings, Pure Appl. Math. Q.7(2011), no. 1, 19–50. [AHMMT] J. Azzam, S. Hofmann, J. M. Martell, M. Mourgoglou, X. Tolsa,Harmonic measure and 2011

[5] xiii+343 pp. [BI] B. Bojarski, T. Iwaniec,Analytical foundations of the theory of quasiconformal mappings inR n, Ann. Acad. Sci. Fenn. Ser. A I Math. 8(2) (1983), 257–324. [BKR] M. Bonk, P . Koskela, 1983

Receipt and verification

First computed	2026-05-18T02:44:17.399628Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e91b64609562427c293d1054e9ed0fe8d286c9ab3dd5490881b0ab1eb64ec576

Aliases

arxiv: 2605.13655 · arxiv_version: 2605.13655v1 · doi: 10.48550/arxiv.2605.13655 · pith_short_12: 5ENWIYEVMJBH · pith_short_16: 5ENWIYEVMJBHYKJ5 · pith_short_8: 5ENWIYEV

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/5ENWIYEVMJBHYKJ5CBKOT3IP5D \
  | 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: e91b64609562427c293d1054e9ed0fe8d286c9ab3dd5490881b0ab1eb64ec576

Canonical record JSON

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    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CV",
    "submitted_at": "2026-05-13T15:14:49Z",
    "title_canon_sha256": "ff49800bebcdb3f1ca5be97efa1c8addd2b554b612b9c2f46d51965c9c4792cd"
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