Oscillation inequalities for Carleson--Dunkl operator

Abstract

In this paper, we establish estimates for the oscillation seminorm for the so-called Carleson--Dunkl operator on weighted $L^p(\mathbb{R},w(x)|x{|}^{2\alpha +1}\mathrm{d}x)$ spaces with power weights $w(x)=|x{|}^{\beta }$. As a result, we obtain oscillation estimates for the standard Carleson operator on $L_{\mathrm{rad}}^p({\mathbb{R}}^n,|x{|}^{\beta }\mathrm{d}x)$. As a byproduct, we obtain a transference principle for radial multipliers on $L_{\mathrm{rad}}^p$ spaces, in the spirit of the Rubio de Francia transference principle.

15 pages, no figures. Incorporated remarks from the reviewers

References in corpus (1)

• Almost Everywhere Convergence of Inverse Dunkl Transform on the Real Line