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

2021/01/11 by Kühn, Franziska, Schilling, René L. · 3 citations
#35K25 #46E35 #60G51 #60J76 #FOS: Mathematics #Functional Analysis (math.FA) #Probability (math.PR)

paper · doi:10.48550/arxiv.2101.03886

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 ∈ \B,F\. Our results apply to a wide class of convolution semigroups including the Gauß--Weierstraß semigroup, stable semigroups and heat kernels for higher-order powers of the Laplacian (-Δ)^m, and we can derive various caloric smoothing estimates.

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