Adams type Dunkl Stein-Weiss inequality on Dunkl Morrey spaces on the real line

TL;DR

This paper extends the classical Adams Stein-Weiss inequality to Dunkl Morrey spaces on the real line, establishing weighted boundedness of Dunkl fractional operators and maximal functions.

Contribution

It introduces the Adams-type Dunkl Stein-Weiss inequality on Dunkl-Morrey spaces, expanding classical results to the Dunkl setting.

Findings

Established weighted boundedness of Dunkl fractional integral operators.

Proved the Adams-type Dunkl Stein-Weiss inequality on Dunkl-Morrey spaces.

Demonstrated the weighted boundedness of Dunkl fractional maximal functions.

Abstract

In this paper, we study the weighted boundedness of the Dunkl fractional integral operator (i.e., Dunkl Stein-Weiss inequality) associated with the Dunkl operator on $\mathbb{R}$. Indeed, we obtain the Adams-type Dunkl Stein-Weiss inequality on Dunkl-Morrey spaces. Our result extends the classical Adams type Stein-Weiss inequality on Morrey space result to the Dunkl setting. Furthermore, we establish the weighted boundedness of the Dunkl fractional maximal function on Dunkl Morrey spaces.