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

作     者：Sibei YANG Dachun YANG Wen YUAN 

作者机构：School of Mathematics and Stat istics Gansu Key Laboratory of Applied Mat hematics and Complex Systems Lanzhou University Lanzhou 730000 China Laboratory of Mathematics and Complex Systems (Ministry of Education of China) School of Mathematical Sciences Beijing Normal University. Beijing 100875 China 

出 版 物：《Frontiers of Mathematics in China》 (中国高等学校学术文摘·数学（英文）)

年 卷 期：2019年第14卷第1期

页      面：177-201页

核心收录：

学科分类：07[理学] 

基　　金：National Natural Science Foundation of China (Grant Nos. 11871254, 11571289. 11571039, 11761131002, 11671185. 11871100) Fundamental Research Funds for the Central Universities (Grant No. lzujbky-2018-111) 

主　　题：Musielak-Orlicz-Sobolev space Orlicz-Sobolev space variable exponent Sobolev space sharp ball averaging function 

摘      要：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. H?st? and A. M. Ribeiro [Commun. Contemp. Math., 2017, 19: 1650022] via weakening the assumption f ∈ L^1(R^n) into f ∈ L^1loc(R^n), which was conjectured to be true by Hosto and Ribeiro in the aforementioned same article.