Littlewood–Paley operators associated with the Dunkl operator on R

Abstract

We consider a vector version of L p -multipliers for the Dunkl transform on R and we prove L p -inequalities for the Littlewood-Paley operators.

Dimension‐free square function estimates for Dunkl operators

“…Despite extensive studies in various settings in literature, we concentrate on square function estimates in the Dunkl setting. For $$p\in (1,2]$$, the $$L^p$$ boundedness of the square function $$G_\nabla$$ for the Dunkl Poisson flow was obtained in [29] on $$\mathbb {R}$$ and in [30] on $$\mathbb {R}^d$$, respectively. By establishing Banach space valued singular integral theory, for all $$p\in (1,\infty )$$, the $$L^p$$ boundedness of $$G_{\nabla _\kappa }$$ for the Dunkl poisson flow on $$\mathbb {R}^d$$ was obtained in [1].…”