Sharp Hardy inequalities of fractional order involving slowly varying functions

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:386

Article

Gurka, Petr¹  Opic, Bohumir² 

[1] Czech Univ Life Sci Prague, Dept Math, Prague 16521 6, Czech Republic

[2] Charles Univ Prague, Fac Math & Phys, Dept Math Anal, Prague 18675 8, Czech Republic

关键词: Hardy inequality of fractional order;    Slowly varying functions;   

DOI  :  10.1016/j.jmaa.2011.08.031

来源: Elsevier

【 摘 要 】

We establish necessary and sufficient conditions for the validity of Hardy inequalities of fractional orders involving weights which are products of power-type functions and slowly varying functions. Consequently, for such weights, we solve Open Problems 1 and 2 mentioned in the book of Kufner and Persson, Weighted Inequalities of Hardy Type (World Scientific Publishing, 2003). (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free