Bounded and compact integral operators

Bibliographic Information

Bounded and compact integral operators

by David E. Edmunds, Vakhtang Kokilashvili, Alexander Meskhi

(Mathematics and its applications, Vol.543)

Kluwer Academic, c2002

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Note

Includes reference (p.622-639) and index

Description and Table of Contents

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).

Table of Contents

Preface. Acknowledgments. Basic notation. 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. Index.

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Details

  • NCID
    BA5717758X
  • ISBN
    • 1402006195
  • Country Code
    ne
  • Title Language Code
    eng
  • Text Language Code
    eng
  • Place of Publication
    Dordrecht
  • Pages/Volumes
    xvi, 643 p.
  • Size
    25 cm
  • Parent Bibliography ID
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