Overview
- Authors:
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David E. Edmunds
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Centre for Mathematical Analysis and its Application, University of Sussex, Sussex, UK
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Vakhtang Kokilashvili
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A. Razmadze Mathematical Institute, Georgian Academy of Sciences, Tbilisi, Georgia
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Alexander Meskhi
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A. Razmadze Mathematical Institute, Georgian Academy of Sciences, Tbilisi, Georgia
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Table of contents (10 chapters)
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- David E. Edmunds, Vakhtang Kokilashvili, Alexander Meskhi
Pages 1-76
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- David E. Edmunds, Vakhtang Kokilashvili, Alexander Meskhi
Pages 77-250
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- David E. Edmunds, Vakhtang Kokilashvili, Alexander Meskhi
Pages 251-316
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- David E. Edmunds, Vakhtang Kokilashvili, Alexander Meskhi
Pages 317-342
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- David E. Edmunds, Vakhtang Kokilashvili, Alexander Meskhi
Pages 343-366
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- David E. Edmunds, Vakhtang Kokilashvili, Alexander Meskhi
Pages 367-446
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- David E. Edmunds, Vakhtang Kokilashvili, Alexander Meskhi
Pages 447-499
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- David E. Edmunds, Vakhtang Kokilashvili, Alexander Meskhi
Pages 501-592
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- David E. Edmunds, Vakhtang Kokilashvili, Alexander Meskhi
Pages 593-615
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- David E. Edmunds, Vakhtang Kokilashvili, Alexander Meskhi
Pages 617-621
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Back Matter
Pages 622-643
About this book
The monograph presents some of the authors' recent and original results concerning boundedness and compactness problems in Banach function spaces both for classical operators and integral transforms defined, generally speaking, on nonhomogeneous spaces. Itfocuses onintegral operators naturally arising in boundary value problems for PDE, the spectral theory of differential operators, continuum and quantum mechanics, stochastic processes etc. The book may be considered as a systematic and detailed analysis of a large class of specific integral operators from the boundedness and compactness point of view. A characteristic feature of the monograph is that most of the statements proved here have the form of criteria. These criteria enable us, for example, togive var ious explicit examples of pairs of weighted Banach function spaces governing boundedness/compactness of a wide class of integral operators. The book has two main parts. The first part, consisting of Chapters 1-5, covers theinvestigation ofclassical operators: Hardy-type transforms, fractional integrals, potentials and maximal functions. Our main goal is to give a complete description of those Banach function spaces in which the above-mentioned operators act boundedly (com pactly). When a given operator is not bounded (compact), for example in some Lebesgue space, we look for weighted spaces where boundedness (compact ness) holds. We develop the ideas and the techniques for the derivation of appropriate conditions, in terms of weights, which are equivalent to bounded ness (compactness).
