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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
Article
  • 20 Downloads

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.

Keywords

Continuous Function Convex Function Russian Translation Maximum Point Mathematical Journal 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  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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