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＜電子ブック＞
Bounded and Compact Integral Operators / by David E. Edmunds, V.M Kokilashvili, Alexander Meskhi
(Mathematics and Its Applications ; 543)

版	1st ed. 2002.
出版者	Dordrecht : Springer Netherlands : Imprint: Springer
出版年	2002
本文言語	英語
大きさ	XVI, 643 p : online resource
著者標目	*Edmunds, David E author Kokilashvili, V.M author Meskhi, Alexander author SpringerLink (Online service)
件　名	LCSH:Potential theory (Mathematics) LCSH:Fourier analysis LCSH:Harmonic analysis LCSH:Mathematical analysis LCSH:Operator theory FREE:Potential Theory FREE:Fourier Analysis FREE:Abstract Harmonic Analysis FREE:Integral Transforms and Operational Calculus FREE:Operator Theory
一般注記	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 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) HTTP:URL=https://doi.org/10.1007/978-94-015-9922-1

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