Bochner-Riesz summability for analytic functions on the m-complex unit sphere and for cylindrically symmetric functions on R^{n-1} times R

Details Bochner-Riesz summability for analytic functions on the m-complex unit sphere and for cylindrically symmetric functions on R^{n-1} times R Bochner-Riesz summability for analytic functions on the m-complex unit sphere and for cylindrically symmetric functions on R^{n-1} times R

2002-07-25

arxiv.org/abs/math/0207225v1

Mathematics

Classical Analysis and ODEs

11 pages, no figures, submitted, Comm. Analysis and Geometry

Scientific paper

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.

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