Ukrainian Mathematical Journal

, Volume 58, Issue 9, pp 1441–1447 | Cite as

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.


Continuous Function Convex Function Russian Translation Maximum Point Mathematical Journal 
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  1. 1.
    G. H. Hardy, J. E. Littlewood, and G. Pólya, Inequalities [Russian translation], Inostrannaya Literatura, Moscow (1948).Google Scholar
  2. 2.
    O. M. Mulyava, “On convergence classes of Dirichlet series,” Ukr. Mat. Zh., 51, No. 11, 1485–1494 (1999).CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • O. M. Mulyava
    • 1
  1. 1.Kyiv National University of Food TechnologyKyiv

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