Smoothing properties of the fractional Gauss-Weierstrass semi-group in Morrey smoothness spaces

Abstract

In this paper we derive caloric smoothing estimates in Morrey smoothness spaces using decomposition techniques by means of wavelets and molecules. Our new estimate extends results for Gauss-Weierstrass, Cauchy-Poisson and fractional Gauss-Weierstrass semigroups.

Keywords

• morrey smoothness spaces of besov and triebel-lizorkin type
• caloric smoothing
• wavelets
• molecules
• fractional gauss-weierstrass semi-group