New characterizations of Morrey spaces and their preduals with applications to fractional Laplace equations

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:266

Article

Liu, Liguang¹  Wu, Suqing²  Yang, Dachun²  Yuan, Wen² 

[1] Renmin Univ China, Sch Math, Beijing 100872, Peoples R China

[2] Beijing Normal Univ, Sch Math Sci, Lab Math & Complex Syst, Minist Educ China, Beijing 100875, Peoples R China

关键词: Riesz potential;    Money space;    Capacity;    Fractional Laplace equation;   

DOI  :  10.1016/j.jde.2018.10.020

来源: Elsevier

【 摘 要 】

In this article, the authors characterize the Money spaces as well as their preduals via quadratic functions related to the Taylor remainder of the kernel of the Riesz potential. As applications, the authors obtain some strong capacitary inequalities, which are then used to study the regularity of the duality/weak solution to the fractional Laplace equation with measure data. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free