Convolution inequalities for Besov and Triebel–Lizorkin spaces, and applications to convolution semigroups

Abstract

We establish convolution inequalities for Besov spaces $B_{p,q}^s$ and Triebel–Lizorkin spaces $F_{p,q}^s$. As an application, we study the mapping properties of convolution semigroups, considered as operators on the function spaces $A_{p,q}^s$, $A \in \{