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Item Details
| Title:
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BOUNDED AND COMPACT INTEGRAL OPERATORS
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| By: |
David Eric Edmunds, Vakhtang Kokilashvilli, Alexander Meskhi |
| Format: |
Hardback |
| List price:
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£97.00 |
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We currently do not stock this item, please contact the publisher directly for
further information.
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| ISBN 10: |
1402006195 |
| ISBN 13: |
9781402006197 |
| Publisher: |
SPRINGER-VERLAG NEW YORK INC. |
| Pub. date: |
31 May, 2002 |
| Edition: |
2002 ed. |
| Series: |
Mathematics and Its Applications 543 |
| Pages: |
643 |
| Description: |
Presents results concerning boundedness and compactness problems in Banach function spaces both for classical operators and integral transforms defined. This book focuses on integral operators naturally arising in boundary value problems for PDE, the spectral theory of differential operators, continuum and quantum mechanics, and more. |
| Synopsis: |
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). |
| Illustrations: |
XVI, 643 p. |
| Publication: |
US |
| Imprint: |
Springer-Verlag New York Inc. |
| Returns: |
Returnable |
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