Boundedness of fractional integrals and fractional derivatives on Laguerre Lipschitz spaces

TL;DR

This paper investigates the boundedness of fractional integrals and derivatives related to Laguerre polynomial expansions on Laguerre Lipschitz spaces, developing Poisson integral theory in this context.

Contribution

It introduces a novel approach to analyze fractional operators on Laguerre Lipschitz spaces using Poisson integral theory.

Findings

Established boundedness results for fractional integrals and derivatives on Laguerre Lipschitz spaces.

Extended Poisson integral theory to the Laguerre setting.

Connected Laguerre Lipschitz space analysis with Gaussian Lipschitz space results.

Abstract

In this paper, we study the boundedness of a class of fractional integrals and derivatives associated with Laguerre polynomial expansions on Laguerre Lipschitz spaces. The consideration of such operators is motivated by the study of corresponding results on Gaussian Lipschitz spaces. The key idea used here is to develop the Poisson integral theory in the Laguerre setting.