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The grand Lusin-area characterization of Hajłasz-Sobolev spaces and Triebel-Lizorkin spaces

Authors

  • Xiaojuan Jiang,

    Corresponding author
    1. School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, People's Republic of China
    • Phone: +86 10 5880 5472, Fax: +86 10 5880 5472
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  • Dachun Yang,

    Corresponding author
    1. School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, People's Republic of China
    • Phone: +86 10 5880 5472, Fax: +86 10 5880 5472
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  • Wen Yuan

    Corresponding author
    1. School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, People's Republic of China
    • Phone: +86 10 5880 5472, Fax: +86 10 5880 5472
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  • Dedicated to Professor Hans Triebel on the occasion of his 75th birthday

Abstract

In this paper, the authors establish the grand Lusin-area characterization of the Hajłasz-Sobolev spaces and, more generally, the Triebel-Lizorkin spaces on both Euclidean spaces and RD-spaces, namely, metric spaces enjoying both doubling and reverse doubling properties.

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