Frontiers of Mathematics in China >
New characterizations of Musielak–Orlicz–Sobolev spaces via sharp ball averaging functions
Received date: 08 Oct 2018
Accepted date: 24 Dec 2018
Published date: 22 Mar 2019
Copyright
We establish a new characterization of the Musielak–Orlicz–Sobolev space on ; 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 into , which was conjectured to be true by Hästö and Ribeiro in the aforementioned same 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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