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Function Spaces and Inequalities pp 15–35Cite as

Sobolev Embeddings for Herz-Type Triebel-Lizorkin Spaces

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Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 206))

Abstract

In this paper we prove the Sobolev embeddings for Herz-type Triebel-Lizorkin spaces,

$$\begin{aligned} \dot{K}_{q}^{\alpha _{2},r}F_{\theta }^{s_{2}}\hookrightarrow \dot{K} _{s}^{\alpha _{1},p}F_{\beta }^{s_{1}} \end{aligned}$$

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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Acknowledgements

The author would like to thank the anonymous reviewers for their valuable comments and suggestions to improve the quality of the paper.

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Authors and Affiliations

  1. Laboratory of Functional Analysis and Geometry of Spaces, Department of Mathematics, M’sila University, P.O. Box 166, 28000, M’sila, Algeria

    Douadi Drihem

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  1. Douadi Drihem
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Correspondence to Douadi Drihem .

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Editors and Affiliations

  1. Department of Mathematics, South Asian University, New Delhi, Delhi, India

    Pankaj Jain

  2. Faculty of Mathematics & Computer Science, Friedrich Schiller University Jena, Jena, Thüringen, Germany

    Hans-Jürgen Schmeisser

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Drihem, D. (2017). Sobolev Embeddings for Herz-Type Triebel-Lizorkin Spaces. In: Jain, P., Schmeisser, HJ. (eds) Function Spaces and Inequalities. Springer Proceedings in Mathematics & Statistics, vol 206. Springer, Singapore. https://doi.org/10.1007/978-981-10-6119-6_2

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