Endpoint bounds of square functions associated with Hankel multipliers
Volume 228 / 2015
Studia Mathematica 228 (2015), 123-151
MSC: Primary 42B15; Secondary 42B25.
DOI: 10.4064/sm228-2-3
Abstract
We prove endpoint bounds for the square function associated with radial Fourier multipliers acting on $L^{p}$ radial functions. This is a consequence of endpoint bounds for a corresponding square function for Hankel multipliers. We obtain a sharp Marcinkiewicz-type multiplier theorem for multivariate Hankel multipliers and $L^p$ bounds of maximal operators generated by Hankel multipliers as corollaries. The proof is built on techniques developed by Garrigós and Seeger for characterizations of Hankel multipliers.
