Integral operators in non-standard function spaces. Volume 1, Variable exponent Lebesgue and Amalgam spaces

• 作者： Kokilashvili, Vakhtang, author.
• 其他作者：
  • Meskhi, Alexander, author.
  • Rafeiro, Humberto, author.
  • Samko, Stefan, author.
  • SpringerLink (Online service)
• 其他題名：
  • Variable exponent Lebesgue and Amalgam spaces
  • Operator theory: advances and applications ;
• 出版： Cham : Springer International Publishing :Imprint: Birkhauser
• 叢書名： Operator theory: advances and applications,volume 248
• 主題： Integral operators. , Algebraic spaces. , Mathematics. , Operator Theory. , Functional Analysis.
• ISBN： 9783319210155 (electronic bk.) 、 9783319210148 (paper)
• FIND@SFXID: CGU
• 資料類型: 電子書
• 內容註: Preface -- I: Variable Exponent Lebesgue and Amalgam spaces -- 1 Hardy Type Operators -- 2 Oscillating weights -- 3 Kernel Integral Operators -- 4 Two-Weight Estimates -- 5 One-sided Operators -- 6 Two-weight Inequalities for Fractional Maximal Functions -- 7 Hypersingular Integrals -- 8 Description of the Range of Potentials 213 -- 9 More on Compactness -- 10 Applications to Singular Integral Equations -- II: Holder Spaces of Variable Order -- 11 Variable Order Holder Spaces -- III: Variable Exponent Morrey-Campanato and Herz Spaces -- 12 Morrey Type Spaces; Constant Exponents -- 13 Morrey Type Spaces; Variable Exponents -- Bibliography -- Symbol Index -- Subject Index.
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• 摘要註: 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 Holder 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.
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