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

  • O. M. Mulyava


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.
How to Cite
Mulyava, O. 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,
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