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Several Hardy Type Inequalities with Weights Related to Generalized Greiner Operator

Published online by Cambridge University Press:  20 November 2018

Pengcheng Niu ,
Yafei Ou  and
Junqiang Han
Pengcheng Niu
Affiliation:
Department of Applied Mathematics, Northwestern Polytechnical University, Xi’an, Shaanxi, 710072, P.R. China e-mail: pengchengniu@yahoo.com.cn e-mail: oyafei@126.com e-mail: southhan@163.com
Yafei Ou
Affiliation:
Department of Applied Mathematics, Northwestern Polytechnical University, Xi’an, Shaanxi, 710072, P.R. China e-mail: pengchengniu@yahoo.com.cn e-mail: oyafei@126.com e-mail: southhan@163.com
Junqiang Han
Affiliation:
Department of Applied Mathematics, Northwestern Polytechnical University, Xi’an, Shaanxi, 710072, P.R. China e-mail: pengchengniu@yahoo.com.cn e-mail: oyafei@126.com e-mail: southhan@163.com
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Abstract

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In this paper, we establish several weighted ${{L}^{p}}\left( 1\,<\,p\,\infty \right)$ Hardy type inequalities related to the generalized Greiner operator by improving the method of Kombe. Then the best constants in inequalities are discussed by introducing new polar coordinates.

Keywords

35B0535H99generalized Greiner operatorpolar coordinatesHardy inequality
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 53 , Issue 1 , 01 March 2010 , pp. 153 - 162
Copyright
Copyright © Canadian Mathematical Society 2010

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