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Revista Matemática Complutense

, Volume 29, Issue 2, pp 341–404 | Cite as

Trace and extension operators for Besov spaces and Triebel–Lizorkin spaces with variable exponents

  • Takahiro NoiEmail author
Article

Abstract

This paper is concerned with the boundedness of trace and extension operators for Besov spaces and Triebel–Lizorkin spaces with variable exponents on the upper half space \({\mathbb R}^n_+\). To define trace and extension operators, we introduce a quarkonial decomposition for Besov spaces and Triebel–Lizorkin spaces with variable exponents on \({\mathbb R}^n\). We then study the continuity of such operators related to \({\mathbb R}^n_+\).

Keywords

Besov space Triebel-Lizorkin space Variable exponents Quarkonial decomposition Trace operator Extension operator 

Mathematics Subject Classification

Primary 42B35 Secondary 41A17 

Notes

Acknowledgments

The author would like to express my gratitude to Professor Yoshikazu Kobayashi for his reading this manuscript carefully and appropriate advice. The author also would like to express my gratitude to Professor Yoshihiro Sawano for sending his book [29]. The author obtained many ideas from the book [29]. The author is thankful to anonymous reviewers for their careful reading of this paper and their comments.

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Copyright information

© Universidad Complutense de Madrid 2016

Authors and Affiliations

  1. 1.Department of Mathematics and Information ScienceTokyo Metropolitan UniversityHachiojiJapan

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