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Israel Journal of Mathematics

, Volume 9, Issue 1, pp 20–26 | Cite as

Two integral inequalities

  • J. R. Blum
  • M. Reichaw
Article

Abstract

Let (X, S, μ) and (Y, T, ν) be two measure spaces,K(g)= Y k(x,y)g(y)dv(y) ξ +=max (ξ,0), and\(\delta (K) = \sup _{x_1 ,x_2 \in X} \int {{}_Y(k(x_1 } y) - (k(x_2 ,y))^ + dv(y)\). Two integral inequalities (the first of which has a simple geometrical interpretation) involvingδ(K) are proved. Generalizations of theorems about infinite stochastic matrices and convergence of superpositions of sequences of integral operators are obtained.

Keywords

Integral Operator Measure Space Ergodic Theorem Integral Inequality Studia Math 
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Copyright information

© The Weizmann Science Press of Israel 1970

Authors and Affiliations

  • J. R. Blum
    • 1
    • 2
  • M. Reichaw
    • 1
    • 2
  1. 1.Technion—Israel Institute of TechnologyHaifa
  2. 2.University of New MexicoAlbuquerque

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