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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.

communications in analysis and geometry

Bochner-Riesz Summability for Analytic Functions on the &lt;i&gt;m&lt;/i&gt;-complex Unit Sphere and for Cylindrically Symmetric Functions on ℝ&lt;sup&gt;n - 1&lt;/sup&gt; x ℝ