Bi-predual spaces of generalized Campanato spaces with variable growth condition

作     者：Satoshi YAMAGUCHI Eiichi NAKAI Katsunori SHIMOMURA 

作者机构：Department of Mathematics Ibaraki University 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报(英文版))

年 卷 期：2024年

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：Supported by Grant-in-Aid for Scientific Research (C)(Grant No. 21K03304)Japan Society for the Promotion of Science the Research Institute for Mathematical Sciences,an International Joint Usage/Research Center located in Kyoto University 

摘      要：In this paper we extend the duality(■)*= H1(Rd) to generalized Campanato spaces with variable growth condition Lp,φ(Rd) instead of BMO(Rd). We also extend the characterization of Cc∞omp(Rd)BMO(Rd)by Uchiyama(1978) to ■. Moreover, using this characterization, we prove the boundedness of singular and fractional integral operators on ■.The function space Lp,φ(Rd) treated in this paper covers the case that it is coincide with Lipαon one area, with BMO on another area and with the Morrey space on the other area, for example.