Communications in Analysis and Geometry

Volume 12 (2004)

Number 1

Bochner-Riesz Summability for Analytic Functions on the m-complex Unit Sphere and for Cylindrically Symmetric Functions on ℝn - 1 x ℝ

Pages: 43 – 57

DOI: http://dx.doi.org/10.4310/CAG.2004.v12.n1.a4

Authors

Adam Sikora

Terrence Tao

Abstract

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

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