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Integral analog of one generalization of the Hardy inequality and its applications

Authors:

O M Mulyava

Institution:

(1) Kyiv National University of Food Technology, Kyiv

Abstract:

Under certain conditions on continuous functions μ, λ, a, and f, we prove the inequality

$\int\limits_0^y {\mu (x)\lambda (x)f\left( {\frac{{\int_0^x {\lambda (t)a(t)dt} }}{{\int_0^x {\lambda (t)dt} }}} \right)dx \leqslant K\int\limits_0^y {\mu (x)\lambda (x)f(a(x))} dx,} y \leqslant \infty ,$

and describe its application to the investigation of the problem of finding conditions under which Laplace integrals belong to a class of convergence. __________ Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 9, pp. 1271–1275, September, 2006.

Keywords:

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