Integral Operators in Non-Standard Function Spaces
Volume 2: Variable Exponent Hölder, Morrey–Campanato and Grand Spaces
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Beschreibung
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 mathematicsand prospective students.
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.
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
Autor*in
Vakhtang Kokilashvili
Themen in »Integral Operators in Non-Standard Function Spaces«
Morrey spaces Morrey-Campanato and Herz spaces Sobolev-type theorem commutators compactness grand Bochner spaces grand Lebesgue spaces grand Morrey spaces grand variable exponent Lebesgue spaces maximal, singular and potential operators product kernels variable Herz spaces variable exponent Hölder spaces variable exponent Morrey spaces
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“The entire book, which is written in a complete consecutive way of presentation of the material, could be considered as a short encyclopedia, very useful for providing a basis for further research in the area.” (Nikos Labropoulos, Mathematical Reviews, August, 2017)
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