Bochner-Riesz Summability for Analytic Functions on the <i>m</i>-complex Unit Sphere and for Cylindrically Symmetric Functions on ℝ<sup>n - 1</sup> x ℝ

We prove that spectral projections of Laplace-Beltrami operator on the m-complex unit sphere E▵_{S^{2m - 1}} ([0, ℝ)) are uniformly bounded as operators from H^p(S^{2m - 1}) to L^p(S^{2m - 1}) for all p ∈ (1,∞). We also show that the Bochner-Riesz conjecture is true when restricted to cylindrically symmetric functions on ℝ^{n - 1} x ℝ.