English

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

Classical Analysis and ODEs 2007-05-23 v1 Spectral Theory

Abstract

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.

Keywords

Cite

@article{arxiv.math/0207225,
  title  = {Bochner-Riesz summability for analytic functions on the m-complex unit sphere and for cylindrically symmetric functions on R^{n-1} times R},
  author = {Adam Sikora and Terence Tao},
  journal= {arXiv preprint arXiv:math/0207225},
  year   = {2007}
}

Comments

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