A multiplier theorem for ultraspherical polynomials
Volume 247 / 2019
Studia Mathematica 247 (2019), 1-43
MSC: Primary 42C10.
DOI: 10.4064/sm8331-2-2018
Published online: 5 November 2018
Abstract
The main concern of this paper is to adapt a result of Garrigós and Seeger (2008) regarding radial $L^{p}$ Fourier multipliers acting on $L^{p}$ radial functions on $\mathbb {R}^{d}$ to $L^{p}$ zonal multipliers acting on zonal functions on the unit sphere $S^{d}$.
