Riesz Potentials, Bessel Potentials, and Fractional Derivatives on Besov-Lipschitz Spaces for the Gaussian Measure

Abstract

Gaussian Lipschitz spaces Lipα(γd) and the boundedness properties of Riesz potentials, Bessel potentials and fractional derivatives there were studied in detail in Gatto and Urbina (On Gaussian Lipschitz Spaces and the Boundedness of Fractional Integrals and Fractional Derivatives on them, 2009. Preprint. arXiv:0911.3962v2). In this chapter we will study the boundedness of those operators on Gaussian Besov-Lipschitz spaces Bp,qα(γd). Also, these results can be extended to the case of Laguerre or Jacobi expansions and even further to the general framework of diffusions semigroups. © Springer Science+Business Media, LLC 2013.