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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.
List of contents
IV: Grand Lebesgue Spaces.- 14 Maximal Functions and Potentials.- 15 Grand Lebesgue Spaces on Sets with Infinite Measure.- V: Grand Morrey Spaces.- 16 Maximal Functions, Fractional and Singular Integrals.- 17 Multiple Operators on the Cone of Decreasing Functions.- A: Grand Bochner Spaces.- Bibliography.- Symbol Index.- Subject Index.IV: Grand Lebesgue Spaces.- 14 Maximal Functions and Potentials.- 15 Grand Lebesgue Spaces on Sets with Infinite Measure.- V: Grand Morrey Spaces.- 16 Maximal Functions, Fractional and Singular Integrals.- 17 Multiple Operators on the Cone of Decreasing Functions.- A: Grand Bochner Spaces.- Bibliography.- Symbol Index.- Subject Index.
Summary
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.
Additional text
“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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"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)
