Bounded and Compact Integral Operators

  • David E. Edmunds
  • Vakhtang Kokilashvili
  • Alexander Meskhi

Part of the Mathematics and Its Applications book series (MAIA, volume 543)

Table of contents

  1. Front Matter
    Pages i-xvi
  2. David E. Edmunds, Vakhtang Kokilashvili, Alexander Meskhi
    Pages 1-76
  3. David E. Edmunds, Vakhtang Kokilashvili, Alexander Meskhi
    Pages 77-250
  4. David E. Edmunds, Vakhtang Kokilashvili, Alexander Meskhi
    Pages 251-316
  5. David E. Edmunds, Vakhtang Kokilashvili, Alexander Meskhi
    Pages 317-342
  6. David E. Edmunds, Vakhtang Kokilashvili, Alexander Meskhi
    Pages 343-366
  7. David E. Edmunds, Vakhtang Kokilashvili, Alexander Meskhi
    Pages 367-446
  8. David E. Edmunds, Vakhtang Kokilashvili, Alexander Meskhi
    Pages 447-499
  9. David E. Edmunds, Vakhtang Kokilashvili, Alexander Meskhi
    Pages 501-592
  10. David E. Edmunds, Vakhtang Kokilashvili, Alexander Meskhi
    Pages 593-615
  11. David E. Edmunds, Vakhtang Kokilashvili, Alexander Meskhi
    Pages 617-621
  12. Back Matter
    Pages 622-643

About this book

Introduction

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).

Keywords

Fourier transform Singular integral compactness differential equation harmonic analysis integral transform maximum measure

Authors and affiliations

  • David E. Edmunds
    • 1
  • Vakhtang Kokilashvili
    • 2
  • Alexander Meskhi
    • 2
  1. 1.Centre for Mathematical Analysis and its ApplicationUniversity of SussexSussexUK
  2. 2.A. Razmadze Mathematical InstituteGeorgian Academy of SciencesTbilisiGeorgia

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-015-9922-1
  • Copyright Information Springer Science+Business Media B.V. 2002
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-90-481-6018-1
  • Online ISBN 978-94-015-9922-1
  • About this book