Pith Number

pith:AXDINFTY

pith:2026:AXDINFTYHFUPTQK7AYPOCPMG4T

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Recovering Hardy spaces from optimal domains of integration operators

Antti Per\"al\"a, Setareh Eskandari

The optimal domain for a bounded Volterra operator Tg from Hp to Hq always strictly contains Hp on the unit ball.

arxiv:2602.11955 v2 · 2026-02-12 · math.CV · math.FA

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Record completeness

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Claims

C1strongest claim

It is shown that the optimal domain of a bounded Tg:Hp→Hq always strictly contains Hp. Moreover, the intersection of the optimal domains is equal to Hp if p≥q, whereas if p<q, this intersection is a genuinely larger tent space of holomorphic functions.

C2weakest assumption

The assumption that Tg is bounded from Hp to Hq together with the standard definitions of Hardy spaces Hp, optimal domains, and tent spaces on the unit ball in several complex variables.

C3one line summary

Optimal domains for Volterra operators Tg: Hp to Hq on the unit ball strictly contain Hp, with their intersection equaling Hp if p greater than or equal to q and a larger tent space if p less than q.

References

24 extracted · 24 resolved · 0 Pith anchors

[1] P. Ahern, J. Bruna, Maximal and area integral characterizations of Hardy-Sobolev spaces in the unit ball ofC n,Rev. Math. Iberoam.,4, 123–153, (1988) 1988

[2] A. A. Albanese, J. Bonet, W. J. Ricker, Optimal domain of Volterra operators in Korenblum spaces., arXiv:2502.00755

[3] A. A. Albanese, J. Bonet, W. J. Ricker, Optimal domain of Volterra operators in classes of Banach spaces of analytic functions., arXiv:2512.06398

[4] A. Aleman, J. Cima, An integral operator onH p and Hardy’s inequality.,Journal d’Analyse Math´ ematique,85, (1), 157–176, (2001) 2001

[5] A. Aleman, A. G. Siskakis, An integral operator onH p.,Complex Variables, Theory and Application: An International Journal.,28, (2), 149–158, (1995) 1995

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-17T23:39:16.203645Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

05c68696783968f9c15f061ee13d86e4ebabd141a433d6085e2f158e3b80c933

Aliases

arxiv: 2602.11955 · arxiv_version: 2602.11955v2 · doi: 10.48550/arxiv.2602.11955 · pith_short_12: AXDINFTYHFUP · pith_short_16: AXDINFTYHFUPTQK7 · pith_short_8: AXDINFTY

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/AXDINFTYHFUPTQK7AYPOCPMG4T \
  | 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: 05c68696783968f9c15f061ee13d86e4ebabd141a433d6085e2f158e3b80c933

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ac3dd1a6af2d73d733e6b7146b1b5eaf202c8510445744434e7092b784fb5f3a",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CV",
    "submitted_at": "2026-02-12T13:49:56Z",
    "title_canon_sha256": "875b2198fddcb9cb22b1da316fbf82d0db9f40e37df3fd4462b66e871995d5b0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2602.11955",
    "kind": "arxiv",
    "version": 2
  }
}