Convergence a.e. of spherical partial Fourier integrals on weighted spaces for radial functions: endpoint estimates
Volume 192 / 2009
Studia Mathematica 192 (2009), 173-194
MSC: 26D10, 42B10.
DOI: 10.4064/sm192-2-5
Abstract
We prove some extrapolation results for operators bounded on radial $L^p$ functions with $p\in (p_0, p_1)$ and deduce some endpoint estimates. We apply our results to prove the almost everywhere convergence of the spherical partial Fourier integrals and to obtain estimates on maximal Bochner–Riesz type operators acting on radial functions in several weighted spaces.
