Bochner-Riesz summability for analytic functions on the m-complex unit sphere and for cylindrically symmetric functions on R^n-1 times R

2002/07/25 by Adam Sikora, Terence Tao, Sikora, Adam +1
Mathematics · #32A35 #42B15 #Advanced Harmonic Analysis Research #Approximation Theory and Sequence Spaces #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Approximation and Integration #Spectral Theory (math.SP) #math.CA #math.SP #msc:32A35 #msc:42B15

paper · pdf · doi:10.48550/arxiv.math/0207225

11 pages, no figures, submitted, Comm. Analysis and Geometry

arxiv created 2002/07/25 · openalex publication_date 2002/07/25 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that spectral projections of Laplace-Beltrami operator on the m-complex unit sphere E_Delta_S^2m-1([0,R)) are uniformly bounded as an operator from H^p(S^2m-1) to L^p(S^2m-1) for all p --> (1,infinity). We also show that the Bochner-Riesz conjecture is true when restricted to cylindrically symmetric functions on R^n-1 times R.

Citations

• The Multiplier Problem for the Ball

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