A generalization of the weighted Hardy inequality for a class of integral operators

A. A. Kalybai

Institute of Mathematics, Ministry of Education and Science of the Republic of Kazakhstan

Abstract: We consider the problem of finding necessary and sufficient conditions for validity of an estimate for a function by some differential operation containing a weight function rather than the ordinary derivative. This operation is referred to as the $\rho$-weighted derivative.

Keywords: Hardy-type estimate, weight function, integral operator.

UDC: 517.51

Received: 16.06.2003

 English version: Siberian Mathematical Journal, 2004, 45:1, 100–111

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