Mathematics and Its Applications

Bounded and Compact Integral Operators

Authors: Edmunds, David E., Kokilashvili, Vakhtang, Meskhi, Alexander

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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).

Table of contents (10 chapters)

  • Hardy-Type Operators

    Edmunds, David E. (et al.)

    Pages 1-76

  • Fractional Integrals on the Line

    Edmunds, David E. (et al.)

    Pages 77-250

  • One-Sided Maximal Functions

    Edmunds, David E. (et al.)

    Pages 251-316

  • Ball Fractional Integrals

    Edmunds, David E. (et al.)

    Pages 317-342

  • Potentials on R N

    Edmunds, David E. (et al.)

    Pages 343-366

Buy this book

eBook $89.00
price for USA in USD (gross)
  • ISBN 978-94-015-9922-1
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $119.99
price for USA in USD
  • ISBN 978-1-4020-0619-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $139.00
price for USA in USD
  • ISBN 978-90-481-6018-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Bounded and Compact Integral Operators
Authors
Series Title
Mathematics and Its Applications
Series Volume
543
Copyright
2002
Publisher
Springer Netherlands
Copyright Holder
Springer Science+Business Media B.V.
eBook ISBN
978-94-015-9922-1
DOI
10.1007/978-94-015-9922-1
Hardcover ISBN
978-1-4020-0619-7
Softcover ISBN
978-90-481-6018-1
Edition Number
1
Number of Pages
XVI, 643
Topics