03892nam 22005655 450 991025407600332120220415201537.03-319-21015-710.1007/978-3-319-21015-5(CKB)3710000000667102(DE-He213)978-3-319-21015-5(MiAaPQ)EBC4526847(PPN)194076679(EXLCZ)99371000000066710220160511d2016 u| 0engurnn#008mamaatxtrdacontentcrdamediacrrdacarrierIntegral operators in non-standard function spaces volume 1: variable exponent Lebesgue and amalgam spaces /by Vakhtang Kokilashvili, Alexander Meskhi, Humberto Rafeiro, Stefan Samko1st ed. 2016.Cham :Springer International Publishing :Imprint: Birkhäuser,2016.1 online resource (XX, 567 p.)Operator Theory: Advances and Applications,0255-0156 ;2483-319-21014-9 Includes bibliographical references and indexes.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: Hölder Spaces of Variable Order -- 11 Variable Order Hölder 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.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.Operator Theory: Advances and Applications,0255-0156 ;248Operator theoryFunctional analysisOperator Theoryhttps://scigraph.springernature.com/ontologies/product-market-codes/M12139Functional Analysishttps://scigraph.springernature.com/ontologies/product-market-codes/M12066Operator theory.Functional analysis.Operator Theory.Functional Analysis.510Kokilashvili Vakhtangauthttp://id.loc.gov/vocabulary/relators/aut60040Meskhi Alexanderauthttp://id.loc.gov/vocabulary/relators/autRafeiro Humbertoauthttp://id.loc.gov/vocabulary/relators/autSamko Stefanauthttp://id.loc.gov/vocabulary/relators/autMiAaPQMiAaPQMiAaPQBOOK9910254076003321Integral Operators in Non-Standard Function Spaces1983098UNINA