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EMBEDDING THEOREM OF THE WEIGHTED SOBOLEV–LORENTZ SPACES

Part of: Linear function spaces and their duals Inequalities

Published online by Cambridge University Press:  10 June 2021

HONGLIANG LI ,
JIANMIAO RUAN  and
QINXIU SUN
HONGLIANG LI
Affiliation:
Department of Mathematics, Zhejiang International Studies University, Hangzhou 310023, China e-mail: honglli@126.com
JIANMIAO RUAN
Affiliation:
Department of Mathematics, Zhejiang International Studies University, Hangzhou 310023, China e-mail: rjmath@163.com
QINXIU SUN
Affiliation:
Department of Mathematics, Zhejiang University of Science and Technology, Hangzhou 310023, China e-mail: qxsun@126.com
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Abstract

Weight criteria for embedding of the weighted Sobolev–Lorentz spaces to the weighted Besov–Lorentz spaces built upon certain mixed norms and iterated rearrangement are investigated. This gives an improvement of some known Sobolev embedding. We achieve the result based on different norm inequalities for the weighted Besov–Lorentz spaces defined in some mixed norms.

MSC classification

Primary: 46E35: Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems 26D10: Inequalities involving derivatives and differential and integral operators
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 64 , Issue 2 , May 2022 , pp. 358 - 375
Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of Glasgow Mathematical Journal Trust

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Footnotes

*

Project supported by the Zhejiang Provincial Natural Science Foundation of China (LY19A010001 and LY18A010015) and the National Natural Science Foundation of China (11961056 and 11771358).

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