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Integral Operators in Non-Standard Function Spaces

  • Book
  • © 2016

Overview

Authors:
  1. Vakhtang Kokilashvili

    1. A. Razmadze Mathematical Institute, I. Javakhishvili Tbilisi State Universit, Tbilisi, Georgia

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  2. Alexander Meskhi

    1. A. Razmadze Mathematical Institute, I. Javakhishvili Tbilisi State Universit, Tbilisi, Georgia

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  3. Humberto Rafeiro

    1. Departamento de Matemáticas, Pontificia Universidad Javeriana, Bogotá D.C., Colombia

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  4. Stefan Samko

    1. Departamento de Matemática, Universidade do Algarve, Faro, Portugal

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  • Presents the first comprehensive account of the two-weight theory of basic integral operators, developed in variable exponent Lebesgue spaces
  • Provides the complete characterizations of Riesz potentials (of functions in variable Lebesgue spaces), weights and space exponents
  • Explores the weak and strong type estimates criteria for fractional and singular integrals
  • Introduces new function spaces that unify variable exponent Lebesgue spaces and grand Lebesgue spaces

Part of the book series: Operator Theory: Advances and Applications (OT, volume 248/249)

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Keywords

  • MSC (2010): 46E30, 47B34, 42B35, 42B20, 42B25
  • function spaces
  • harmonic analysis
  • integral operators
  • variable exponents

About this book

This two-volume set, the result of the authors’ long and fruitful collaboration, focuses on integral operators in new, non-standard function spaces and presents a systematic study of the boundedness and compactness properties of basic, harmonic analysis integral operators in the following function spaces, among others: variable exponent Lebesgue and amalgam spaces, variable Hölder spaces, variable exponent Campanato, Morrey and Herz spaces, Iwaniec-Sbordone (grand Lebesgue) spaces, grand variable exponent Lebesgue spaces unifying the two spaces mentioned above, grand Morrey spaces, generalized grand Morrey spaces, and weighted analogues of some of them.

The results obtained are widely applied to non-linear PDEs, singular integrals and PDO theory. One of the book’s most distinctive features is that the majority of the statements proved here are in the form of criteria.

It is intended for a broad audience, ranging from researchers in the area to experts in applied mathematics and prospective students.

Authors and Affiliations

  • A. Razmadze Mathematical Institute, I. Javakhishvili Tbilisi State Universit, Tbilisi, Georgia

    Vakhtang Kokilashvili, Alexander Meskhi

  • Departamento de Matemáticas, Pontificia Universidad Javeriana, Bogotá D.C., Colombia

    Humberto Rafeiro

  • Departamento de Matemática, Universidade do Algarve, Faro, Portugal

    Stefan Samko

Bibliographic Information

  • Book Title: Integral Operators in Non-Standard Function Spaces

  • Authors: Vakhtang Kokilashvili, Alexander Meskhi, Humberto Rafeiro, Stefan Samko

  • Series Title: Operator Theory: Advances and Applications

  • Publisher: Birkhäuser Cham

  • Copyright Information: Springer International Publishing Switzerland 2016

  • Series ISSN: 0255-0156

  • Series E-ISSN: 2296-4878

  • Edition Number: 1

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