Riesz Potentials, Bessel Potentials and Fractional Derivatives on Besov-Lipschtz spaces for the Gaussian Measure

TL;DR

This paper investigates the boundedness properties of Riesz potentials, Bessel potentials, and fractional derivatives on Gaussian Besov-Lipschitz spaces, with extensions to other orthogonal expansions and diffusion semigroups.

Contribution

It provides new boundedness results for these operators on Gaussian Besov-Lipschitz spaces, extending to Laguerre, Jacobi expansions, and general diffusion semigroups.

Findings

Boundedness of Riesz potentials on Gaussian Besov-Lipschitz spaces

Boundedness of Bessel potentials on Gaussian Besov-Lipschitz spaces

Extension of results to Laguerre, Jacobi expansions, and diffusion semigroups

Abstract

In this paper we will study the boundedness of Riesz Potentials, Bessel potentials and Fractional Derivatives on Gaussian Besov-Lipschitz spaces $B_{p,q}^{\alpha}(\gamma_d)$. Also these results can be extended to the case of Laguerre or Jacobi expansions and even further to the general framework of diffusions semigroups.