2018
Том 70
№ 8

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

Mulyava O. M.

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.

English version (Springer): Ukrainian Mathematical Journal 58 (2006), no. 9, pp 1441-1447.

Citation Example: Mulyava O. M. Integral analog of one generalization of the Hardy inequality and its applications // Ukr. Mat. Zh. - 2006. - 58, № 9. - pp. 1271–1275.

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