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Sobolev embeddings for Herz-type Triebel-Lizorkin spaces (1502.06417v2)

Published 23 Feb 2015 in math.FA

Abstract: In this paper we prove the Sobolev embeddings for Herz-type Triebel-Lizorkin spaces, \begin{equation*} \dot{K}{q}{\alpha{2},r}F_{\theta }{s_{2}}\hookrightarrow \dot{K}%{s}{\alpha{1},p}F_{\beta }{s_{1}} \end{equation*} where the parameters $\alpha_{1},\alpha_{2},s_{1},s_{2},s,q,r,p,\beta $ and $\theta $ satisfy some suitable conditions. An application we obtain new embeddings between Herz and Triebel-Lizorkin spaces. Moreover, we present the Sobolev embeddings for Triebel-Lizorkin spaces equipped with power weights. All these results cover the results on classical Triebel-Lizorkin spaces.

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