A multiplier theorem for the Hankel transform on the associated Hardy space
Volume 243 / 2018
Studia Mathematica 243 (2018), 1-12
MSC: Primary 42C15; Secondary 42B30, 42B15.
DOI: 10.4064/sm8161-7-2017
Published online: 5 February 2018
Abstract
We prove a multiplier theorem for the Hankel transform $H_{\nu }$ from $H_{A_{\nu }}(0,\infty )$, the Hardy space associated with the Bessel differential operator $A_{\nu }$, into $H_{\nu }L^q(0,\infty ):=\{H_{\nu }f:f\in L^q(0,\infty )\}$. As a consequence an extension of the Paley inequality for the Hankel transform is obtained.
