Boundedness of fractional integrals and fractional derivatives on Laguerre Lipschitz spaces

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.