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# Several Hardy Type Inequalities with Weights Related to Generalized Greiner Operator

Published:2009-12-04
Printed: Mar 2010
• Pengcheng Niu
• Yafei Ou
• Junqiang Han
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## Abstract

In this paper, we establish several weighted $L^p (1\lt p \lt \infty)$ 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: generalized Greiner operator, polar coordinates, Hardy inequality
 MSC Classifications: 35B05 - Oscillation, zeros of solutions, mean value theorems, etc. 35H99 - None of the above, but in this section