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arXiv · 2101.03886

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

Franziska Kühn·René L. Schilling
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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 $A_{p,q}^s$, $A \in \{B,F\}$. Our results apply to a wide class of convolution semigroups including the Gau{\ss}--Weierstra{\ss} semigroup, stable semigroups and heat kernels for higher-order powers of the Laplacian $(-\Delta)^m$, and we can derive various caloric smoothing estimates.

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Franziska Kühn, René L. Schilling. 2021-01-11. Convolution inequalities for Besov and Triebel--Lizorkin spaces, and applications to convolution semigroups. https://arxiv.org/abs/2101.03886

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