Some Embeddings into the Multiplier Spaces Associated to Besov and Lizorkin-Triebel Spaces

Abstract

We study the set of pointwise multipliers in the Lizorkin-Triebel space $F^{s,q}_p$ and of the corresponding multiplier set in the Besov space $B^{s,q}_p$, where we give sufficient conditions on the parameters $s$, $p$ and $p_1$ such that the embeddings $F^{n/p_1,\infty}_{p_1} \cap L^\infty \hookrightarrow M(F^{s,q}_p)$ and $B^{n/p_1, \infty}_{p_1} \hookrightarrow M(B^{s,q}_p)$ hold.