We prove an almost everywhere convergence result for Bochner–Riesz means of (Formula presented.) functions on Heisenberg-type groups, yielding the existence of a (Formula presented.) for which convergence holds for means of arbitrarily small order. The proof hinges on a reduction of weighted (Formula presented.) 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.
Almost everywhere convergence of Bochner–Riesz means on Heisenberg-type groups / Horwich, A. D.; Martini, A.. - In: JOURNAL OF THE LONDON MATHEMATICAL SOCIETY. - ISSN 0024-6107. - STAMPA. - 103:3(2021), pp. 1066-1119. [10.1112/jlms.12401]
Almost everywhere convergence of Bochner–Riesz means on Heisenberg-type groups
Martini A.
2021
Abstract
We prove an almost everywhere convergence result for Bochner–Riesz means of (Formula presented.) functions on Heisenberg-type groups, yielding the existence of a (Formula presented.) for which convergence holds for means of arbitrarily small order. The proof hinges on a reduction of weighted (Formula presented.) 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.File | Dimensione | Formato | |
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Journal of London Math Soc - 2020 - Horwich - Almost everywhere convergence of Bochner Riesz means on Heisenberg%u2010type.pdf
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https://hdl.handle.net/11583/2949508