Almost everywhere convergence of Bochner-Riesz means on Heisenberg-type groups

Adam Horwich; Alessio Martini

doi:10.1112/jlms.12401

Almost everywhere convergence of Bochner-Riesz means on Heisenberg-type groups

Adam Horwich, Alessio Martini

Mathematics

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Abstract

We prove an almost everywhere convergence result for Bochner–Riesz means of L p functions on Heisenberg‐type groups, yielding the existence of a p > 2 for which convergence holds for means of arbitrarily small order. The proof hinges on a reduction of weighted L 2 estimates for the maximal Bochner–Riesz operator to corresponding estimates for the non‐maximal operator, and a ‘dual Sobolev trace lemma’, whose proof is based on refined estimates for Jacobi polynomials.

Original language	English
Pages (from-to)	1066-1119
Journal	Journal of the London Mathematical Society
Volume	103
Issue number	3
Early online date	23 Nov 2020
DOIs	https://doi.org/10.1112/jlms.12401
Publication status	Published - 3 Apr 2021

Keywords

22E30
43A80 (primary)

ASJC Scopus subject areas

Mathematics(all)

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10.1112/jlms.12401Licence: Creative Commons: Attribution (CC BY)

HorwichA2020Almost
This is the accepted version of the following article: Horwich, A.D. and Martini, A. (2020), Almost everywhere convergence of Bochner–Riesz means on Heisenberg‐type groups. J. London Math. Soc.. https://doi.org/10.1112/jlms.12401, which has been published in final form at https://doi.org/10.1112/jlms.12401
Final published version, 892 KBLicence: Creative Commons: Attribution (CC BY)

Sub-Elliptic Harmonic Analysis
Martini, A.
Engineering & Physical Science Research Council
1/01/17 → 31/12/18
Project: Research Councils

Cite this

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abstract = "We prove an almost everywhere convergence result for Bochner–Riesz means of L p functions on Heisenberg‐type groups, yielding the existence of a p > 2 for which convergence holds for means of arbitrarily small order. The proof hinges on a reduction of weighted L 2 estimates for the maximal Bochner–Riesz operator to corresponding estimates for the non‐maximal operator, and a {\textquoteleft}dual Sobolev trace lemma{\textquoteright}, whose proof is based on refined estimates for Jacobi polynomials.",

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Almost everywhere convergence of Bochner-Riesz means on Heisenberg-type groups

Abstract

Keywords

ASJC Scopus subject areas

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Sub-Elliptic Harmonic Analysis

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