On Hardy-type integral inequalities in the whole plane related to the extended Hurwitz-zeta function

Journal of inequalities and applications

article

Michael Th. Rassias¹  Bicheng Yang³  Andrei Raigorodskii⁴ 

[1] Institute of Mathematics, University of Zurich;Program in Interdisciplinary Studies, Institute for Advanced Study;Department of Mathematics, Guangdong University of Education;Moscow Institute of Physics and Technology;Moscow State University;Buryat State University;Caucasus Mathematical Center, Adyghe State University

关键词: Hardy-type integral inequality;    Weight function;    Equivalent form;    Operator;    Hurwitz-zeta function;   

DOI  :  10.1186/s13660-020-02365-1

学科分类：电力

来源: SpringerOpen

【 摘 要 】

Using weight functions, we establish a few equivalent statements of two kinds of Hardy-type integral inequalities with nonhomogeneous kernel in the whole plane. The constant factors related to the extended Hurwitz-zeta function are proved to be the best possible. In the form of applications, we deduce some special cases involving homogeneous kernel. We additionally consider some particular inequalities and operator expressions.

【 授权许可】

CC BY