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 $F_p^{s,q}$ and of the corresponding multiplier set in the Besov space $B_p^{s,q}$, where we give sufficient conditions on the parameters $s$, $p$ and $p_1$ such that the embeddings $F_{p_1}^{n/p_1,\infty }\cap L^{\infty }\hookrightarrow M(F_p^{s,q})$ and $B_{p_1}^{n/p_1,\infty }\hookrightarrow M(B_p^{s,q})$ hold.