Pith Number

pith:W7RFDWV4

pith:2026:W7RFDWV4PSYZ6R7HSOH54M57TM

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A new proof of maximal theorem on Heisenberg groups

Chuhan Sun, Zipeng Wang

New proof shows the strong maximal operator is L^p bounded on Heisenberg groups with bound independent of dimension

arxiv:2605.14961 v1 · 2026-05-14 · math.CA

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\pithnumber{W7RFDWV4PSYZ6R7HSOH54M57TM}

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4 Citations open

5 Replications open

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Claims

C1strongest claim

We give a new proof for the L^p-boundedness of the strong maximal operator defined on (2n+1)-dimensional real Heisenberg groups by using a geometric covering lemma due to Cordoba and Fefferman. Furthermore... the regarding L^p-norm inequality is independent of n.

C2weakest assumption

That the Cordoba-Fefferman geometric covering lemma applies directly to the adapted rectangles on the Heisenberg group without additional geometric adjustments that might depend on n.

C3one line summary

New proof of L^p boundedness for the strong maximal operator on Heisenberg groups, plus dimension-free estimate for 3-parameter dilations via Bourgain's result.

References

10 extracted · 10 resolved · 0 Pith anchors

[1] Bourgain, On the ^p -bounds for maximal functions associated to convex bodies in ^n , Israel Journal of Mathematics, 54 : no.3, 257-265,1986 1986

[2] Bourgain, On the Hardy-Littlewood maximal function for the cube , Israel Journal of Mathematics, 203 : no.1, 275-293, 2014 2014

[3] C\' o rdoba and R 1975

[4] Christ, Hilbert transforms along curves 1985

[5] Christ, The strong maximal function on a nilpotent group , Transactions of the American Mathematical Society 331 : no.1, 1-13, 1992 1992

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-17T23:38:55.285593Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b7e251dabc7cb19f47e7938fde33bf9b30f62deb02ed0aee17888947bb516fdc

Aliases

arxiv: 2605.14961 · arxiv_version: 2605.14961v1 · doi: 10.48550/arxiv.2605.14961 · pith_short_12: W7RFDWV4PSYZ · pith_short_16: W7RFDWV4PSYZ6R7H · pith_short_8: W7RFDWV4

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/W7RFDWV4PSYZ6R7HSOH54M57TM \
  | 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: b7e251dabc7cb19f47e7938fde33bf9b30f62deb02ed0aee17888947bb516fdc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "80300a7845951c9b98b8ec34f45686c1671fb1ab8022f2bc8c34235572514c16",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2026-05-14T15:28:15Z",
    "title_canon_sha256": "6c6da1cb2916405257710ec8026dbdddc5a37e3e19ecae45179607696159033a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.14961",
    "kind": "arxiv",
    "version": 1
  }
}