Integral Operators in Non-Standard Function Spaces
Volume 1: Variable Exponent Lebesgue and Amalgam 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 mathematicsand 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«
Calderón-Zygmund singular integrals Hardy type operators Hölder spaces compactness extrapolation fractional integrals hypersingular integrals kernel operator one-sided operators quasimetric measure spaces two-weight estimates variable exponent Lebesgue spaces weights
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“The book is intended for researchers working in diverse branches of analysis and its applications.” (Boris Rubin, zbMATH 1385.47001, 2018)
“The entire book presents a complete picture of the area in a consecutive way. It could be seen as a short encyclopedia that is very useful as a basis for deeper study but also for further research in the area.” (Nikos Labropoulos, Mathematical Reviews, August, 2017)
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