RESEARCH ARTICLE

New characterizations of Musielak–Orlicz–Sobolev spaces via sharp ball averaging functions

  • Sibei YANG 1 ,
  • Dachun YANG , 2 ,
  • Wen YUAN 2
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  • 1. School of Mathematics and Statistics, Gansu Key Laboratory of Applied Mathematics and Complex Systems, Lanzhou University, Lanzhou 730000, China
  • 2. Laboratory of Mathematics and Complex Systems (Ministry of Education of China), School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China

Received date: 08 Oct 2018

Accepted date: 24 Dec 2018

Published date: 22 Mar 2019

Copyright

2019 Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature

Abstract

We establish a new characterization of the Musielak–Orlicz–Sobolev space on n; which includes the classical Orlicz–Sobolev space, the weighted Sobolev space, and the variable exponent Sobolev space as special cases, in terms of sharp ball averaging functions. Even in a special case, namely, the variable exponent Sobolev space, the obtained result in this article improves the corresponding result obtained by P. Hästö and A. M. Ribeiro [Commun. Contemp. Math., 2017, 19: 1650022] via weakening the assumption fL1(n) into fL 1(n), which was conjectured to be true by Hästö and Ribeiro in the aforementioned same article.

Cite this article

Sibei YANG , Dachun YANG , Wen YUAN . New characterizations of Musielak–Orlicz–Sobolev spaces via sharp ball averaging functions[J]. Frontiers of Mathematics in China, 2019 , 14(1) : 177 -201 . DOI: 10.1007/s11464-019-0744-1

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