Sobolev embeddings for Herz-type Triebel-Lizorkin spaces

Abstract

In this paper we prove the Sobolev embeddings for Herz-type Triebel-Lizorkin spaces, \begin{equation*} \dot{K}_{q}^{α_{2},r}F_{θ}^{s_{2}}\hookrightarrow \dot{K}%_{s}^{α_{1},p}F_{β}^{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.

arXiv commentWe reprove Theorem 2 and we add some embeddings between Herz and Triebel-Lizorkin spaces