Pith Number

pith:JPJKUDBJ

pith:2026:JPJKUDBJ4JSCVENZWCVOOEYAPQ

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A Banach space that distinguishes two maximal operators

Vjekoslav Kova\v{c}

There exists a translation-invariant Banach space of locally integrable functions on which M^diamond is bounded but the sharp maximal operator M^sharp is not.

arxiv:2605.17663 v1 · 2026-05-17 · math.CA · math.FA

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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

We construct a translation-invariant Banach space of locally integrable functions on which M^diamond is bounded, but the sharp maximal operator M^sharp is not.

C2weakest assumption

The space constructed in the paper is a genuine Banach space that is translation-invariant and the boundedness claims for the two operators hold under the definitions given by Maz'ya and Shaposhnikova (abstract).

C3one line summary

A translation-invariant Banach space is constructed on which the non-classical maximal operator M^diamond is bounded but the sharp maximal operator M^sharp is not.

References

44 extracted · 44 resolved · 0 Pith anchors

[1] Maximal functions in Sobolev spaces 2009

[2] Klein, Absolutely continuous spectrum in the Anders on model on the Bethe lattice, Math 2023 · doi:10.4310/mrl

[3] Regularity of the centered fractional maximal function on radial functions 2020 · doi:10.1016/j.jfa.2020.108686

[4] Endpoint Sobolev continuity of the fractional maximal function in higher dimensions.Int 2021 · doi:10.1093/imrn/rnz281

[5] Regularity of fractional maximal functions through Fourier multipliers.J 2019 · doi:10.1016/j.jfa.2018.11.004

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:04:51.555149Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4bd2aa0c29e2642a91b9b0aae713007c0645f68ffc248a2a878358b62a815391

Aliases

arxiv: 2605.17663 · arxiv_version: 2605.17663v1 · doi: 10.48550/arxiv.2605.17663 · pith_short_12: JPJKUDBJ4JSC · pith_short_16: JPJKUDBJ4JSCVENZ · pith_short_8: JPJKUDBJ

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/JPJKUDBJ4JSCVENZWCVOOEYAPQ \
  | 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: 4bd2aa0c29e2642a91b9b0aae713007c0645f68ffc248a2a878358b62a815391

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a363824dbb427bac459270f8a66816a690ebdd2c648205e741e4c2d4bc846ab1",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2026-05-17T21:47:50Z",
    "title_canon_sha256": "d5119d1fc0e710fbc76f38d541cf3a4c8fa0aa0bc93a4f37997e033452bcea62"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.17663",
    "kind": "arxiv",
    "version": 1
  }
}