Bochner-Riesz summability for analytic functions on the m-complex unit sphere and for cylindrically symmetric functions on ℝn-1 × ℝ

Adam Sikora*, Terence Tao

*Corresponding author for this work

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

We prove that spectral projections of Laplace-Beltrami operator on the m-complex unit sphere EΔS2m-1 ([0, R)) are uniformly bounded as operators from HP(S2m-1) to Lp(S 2m-1) for all p ∈ (1, ∈). We also show that the Bochner-Riesz conjecture is true when restricted to cylindrically symmetric functions on ℝn-1 × ℝ.

Original languageEnglish
Pages (from-to)43-57
Number of pages15
JournalCommunications in Analysis and Geometry
Volume12
Issue number1-2
Publication statusPublished - Jan 2004
Externally publishedYes

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