Hardy-Littlewood maximal, generalized Bessel-Riesz and generalized fractional integral operators in generalized Morrey and $BMO_\phi$ spaces associated with Dunkl operator on the real line

TL;DR

This paper investigates the boundedness of various integral and maximal operators related to Dunkl operators within generalized Morrey and BMO spaces on the real line, expanding the harmonic analysis framework in this setting.

Contribution

It establishes the boundedness of several Dunkl-related operators on generalized Morrey and BMO spaces, providing new insights into Dunkl harmonic analysis.

Findings

Boundedness of Hardy-Littlewood maximal operators in Dunkl-Morrey spaces

Boundedness of Bessel-Riesz and fractional integral operators in Dunkl spaces

Extension to Dunkl-type BMO spaces for fractional integrals

Abstract

The analysis of Morrey spaces, generalized Morrey spaces and $BMO_\phi$ spaces related to the Dunkl operators on $\mathbb{R}$ are covered in this paper. We prove the boundedness of the Hardy-Littlewood maximal operators, Bessel-Riesz operators, generalized Bessel-Riesz operators, and generalized fractional integral operators associated with Dunkl operators on $\mathbb{R}$ in the generalized Dunkl-type Morrey spaces. Further, we derive the boundedness of the modified version of the generalized fractional integral operators associated with the Dunkl operators on $\mathbb{R}$ in Dunkl-type $BMO_\phi$ spaces.