On radial Fourier multipliers and almost everywhere convergence

Abstract

We study a.e. convergence on $L^p$, and Lorentz spaces $L^{p,q}$, $p>\frac{2d}{d-1}$, for variants of Riesz means at the critical index $d(\frac{1}{2}-\frac{1}{p})-\frac{1}{2}$. We derive more general results for (quasi-)radial Fourier multipliers and associated maximal functions, acting on $L^2$ spaces with power weights, and their interpolation spaces. We also include a characterization of boundedness of such multiplier transformations on weighted $L^2$ spaces, and a sharp endpoint bound for Stein's square-function associated with the Riesz means.

References in corpus (1)

• Improved bounds for Stein's square functions

Cited by in corpus (5)

• Square function estimates for the Bochner-Riesz means
• Multi-scale sparse domination
• Almost everywhere convergence of Bochner-Riesz means on Heisenberg-type groups
• Endpoint bounds for quasiradial Fourier multipliers
• Weighted decoupling estimates and the Bochner-Riesz means