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

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.