New Gaussian Riesz transforms on variable Lebesgue spaces

Abstract

We give sufficient conditions on the exponent $p:{\mathbb{R}}^d\to [1,\infty )$ for the boundedness of the non-centered Gaussian maximal function on variable Lebesgue spaces $L^{p(\cdot )}({\mathbb{R}}^d,{\gamma }_d)$, as well as of the new higher order Riesz transforms associated with the Ornstein-Uhlenbeck semigroup, which are the natural extensions of the supplementary first order Gaussian Riesz transforms defined by A. Nowak and K. Stempak in \cite{nowakstempak}.

27 pages, to appear in Analysis Mathematica

References in corpus (1)

• Dimension-free $L^p$ estimates for vectors of Riesz transforms associated with orthogonal expansions