On Gaussian Lipschitz spaces and the boundedness of Fractional Integrals and Fractional Derivatives on them

TL;DR

This paper introduces Gaussian Lipschitz spaces and investigates the boundedness of fractional integral and derivative operators on these spaces, providing new proofs and extending results to Laguerre and Jacobi expansions.

Contribution

It defines Gaussian Lipschitz spaces and analyzes the boundedness of fractional operators, offering alternative proofs and broader applicability to classical and special function expansions.

Findings

Fractional integrals and derivatives are bounded on Gaussian Lipschitz spaces.

Methods extend classical results and apply to Laguerre and Jacobi expansions.

Provides new proofs for known boundedness results.

Abstract

In this paper we introduce Lipschitz spaces with respect to the Gaussian measure, and study the boundedness of the fractional integral and fractional derivative operators on them.The methods are general enough to provide alternative proofs of the ones given in the classical case and moreover can be extended to the case of Laguerre and Jacobi expansions too