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CRITERIA FOR THE BOUNDEDNESS AND COMPACTNESS OF INTEGRAL TRANSFORMS WITH POSITIVE KERNELS

Published online by Cambridge University Press:  20 January 2009

A. Meskhi
A. Meskhi
Affiliation:
A. Razmadze Mathematical Institute, Georgian Academy of Sciences, 1 M. Aleksidze St., Tbilisi 380093, Georgia (meskhi@rmi.acnet.ge)
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Abstract

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The necessary and sufficient conditions that guarantee the boundedness and compactness of integral operators with positive kernels from $L^p(a,b)$ to $L^q_{\nu}(a,b)$, where $p,q\in(1,\infty)$ or $0lt q\leq1lt plt\infty$, for a non-negative Borel measure $\nu$ on $(a,b)$ are found.

AMS 2000 Mathematics subject classification: Primary 46B50; 47B34; 47B38

Keywords

boundednesscompactnessweightoperators with positive kernelsmeasure of non-compactness
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 44 , Issue 2 , June 2001 , pp. 267 - 284
Copyright
Copyright © Edinburgh Mathematical Society 2001