FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

1999, VOLUME 5, NUMBER 2, PAGES 475-491

On integral operators in $L$_p-spaces

A. G. Kostyuchenko
E. D. Nursultanov

Abstract

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On the model problem the influence of mutual disposition of singularities of the integral operator's kernel onto its norm and spectral radius is studied. The upper and lower estimations of norm of integral operators in Lorentz spaces are obtained. On the basis of these inequalities, the partial order relation is introduced that permits in some cases to compare the norms of integral operators.

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Last modified: July 6, 1999