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Integral Operators in Non-Standard Function Spaces

Volume 2: Variable Exponent Hölder, Morrey–Campanato and Grand Spaces

Integral Operators in Non-Standard Function Spaces by Vakhtang Kokilashvili
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This book, 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.

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

Springer International Publishing; May 2016
455 pages; ISBN 9783319210186
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Title: Integral Operators in Non-Standard Function Spaces
Author: Vakhtang Kokilashvili; Alexander Meskhi; Humberto Rafeiro; Stefan Samko
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