Besov-Type Spaces on $R^d$ and Integrability for the Dunkl Transform

TL;DR

This paper investigates Besov-Dunkl spaces on R^d, establishing their properties, characterizations, and the integrability of the Dunkl transform for functions within these spaces.

Contribution

It introduces new characterizations and interpolation formulas for Besov-Dunkl spaces, and explores the integrability of the Dunkl transform in this context.

Findings

Schwartz space is dense in Besov-Dunkl spaces.

An interpolation formula for Besov-Dunkl spaces is proven.

Results on the integrability of the Dunkl transform are established.

Abstract

In this paper, we show the inclusion and the density of the Schwartz space in Besov-Dunkl spaces and we prove an interpolation formula for these spaces by the real method. We give another characterization for these spaces by convolution. Finally, we establish further results concerning integrability of the Dunkl transform of function in a suitable Besov-Dunkl space.