
Bounded and Compact Integral Operators
Kluwer Academic Publishers
Published on 31. May 2002
Book
Hardback
XVI, 643 pages
978-1-4020-0619-7 (ISBN)
Description
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).
More details
Series
Edition
2002 ed.
Language
English
Place of publication
Dordrecht
Netherlands
Target group
Professional and scholarly
Research
Illustrations
XVI, 643 p.
Dimensions
Height: 241 mm
Width: 160 mm
Thickness: 40 mm
Weight
1150 gr
ISBN-13
978-1-4020-0619-7 (9781402006197)
DOI
10.1007/978-94-015-9922-1
Schweitzer Classification
Other editions
Additional editions

David E. Edmunds | V.M Kokilashvili | Alexander Meskhi
Bounded and Compact Integral Operators
Book
12/2010
Springer
€53.49
Shipment within 15-20 days
Content
1. Hardy-Type Operators.- 2. Fractional Integrals on the Line.- 3. One-Sided Maximal Functions.- 4. Ball Fractional Integrals.- 5. Potentials on RN.- 6. Fractional Integrals on Measure Spaces.- 7. Singular Numbers.- 8. Singular Integrals.- 9. Multipliers of Fourier Transforms.- 10. Problems.- References.