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

  • O. M. Mulyava

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.
Published
25.09.2006
How to Cite
MulyavaO. M. “Integral Analog of One Generalization of the Hardy Inequality and Its Applications”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, no. 9, Sept. 2006, pp. 1271–1275, https://umj.imath.kiev.ua/index.php/umj/article/view/3528.
Section
Short communications