LEADER 04210nam 2200565 450 001 996511863003316 005 20231009145543.0 010 $a981-19-6788-1 024 7 $a10.1007/978-981-19-6788-7 035 $a(MiAaPQ)EBC7201832 035 $a(Au-PeEL)EBL7201832 035 $a(CKB)26155069400041 035 $a(DE-He213)978-981-19-6788-7 035 $a(PPN)268063168 035 $a(EXLCZ)9926155069400041 100 $a20230515d2022 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aReal-Variable Theory of Hardy Spaces Associated with Generalized Herz Spaces of Rafeiro and Samko /$fYinqin Li, Dachun Yang, and Long Huang 205 $a1st ed. 2022. 210 1$aSingapore :$cSpringer Nature Singapore Pte Ltd.,$d[2022] 210 4$d©2022 215 $a1 online resource (663 pages) 225 1 $aLecture Notes in Mathematics Series ;$vVolume 2320 311 08$aPrint version: Li, Yinqin Real-Variable Theory of Hardy Spaces Associated with Generalized Herz Spaces of Rafeiro and Samko Singapore : Springer,c2023 9789811967870 320 $aIncludes bibliographical references and index. 327 $a1 Generalized Herz Spaces of Rafeiro and Samko -- 2 Block Spaces and Their Applications -- 3 Boundedness and Compactness Characterizations of Commutators on Generalized Herz Spaces -- 4 Generalized Herz?Hardy Spaces -- 5 Localized Generalized Herz?Hardy Spaces -- 6 Weak Generalized Herz?Hardy Spaces -- 7 Inhomogeneous Generalized Herz Spaces and Inhomogeneous Block Spaces -- 8 Hardy Spaces Associated with Inhomogeneous Generalized Herz Spaces. 330 $aThe real-variable theory of function spaces has always been at the core of harmonic analysis. In particular, the real-variable theory of the Hardy space is a fundamental tool of harmonic analysis, with applications and connections to complex analysis, partial differential equations, and functional analysis. This book is devoted to exploring properties of generalized Herz spaces and establishing a complete real-variable theory of Hardy spaces associated with local and global generalized Herz spaces via a totally fresh perspective. This means that the authors view these generalized Herz spaces as special cases of ball quasi-Banach function spaces. In this book, the authors first give some basic properties of generalized Herz spaces and obtain the boundedness and the compactness characterizations of commutators on them. Then the authors introduce the associated Herz?Hardy spaces, localized Herz?Hardy spaces, and weak Herz?Hardy spaces, and develop a complete real-variable theory of these Herz?Hardy spaces, including their various maximal function, atomic, molecular as well as various Littlewood?Paley function characterizations. As applications, the authors establish the boundedness of some important operators arising from harmonic analysis on these Herz?Hardy spaces. Finally, the inhomogeneous Herz?Hardy spaces and their complete real-variable theory are also investigated. With the fresh perspective and the improved conclusions on the real-variable theory of Hardy spaces associated with ball quasi-Banach function spaces, all the obtained results of this book are new and their related exponents are sharp. This book will be appealing to researchers and graduate students who are interested in function spaces and their applications. 410 0$aLecture Notes in Mathematics ;$vVolume 2320. 606 $aFourier analysis 606 $aEspais de Hardy$2thub 606 $aAnàlisi de Fourier$2thub 608 $aLlibres electrònics$2thub 615 0$aFourier analysis. 615 7$aEspais de Hardy 615 7$aAnàlisi de Fourier 676 $a515.2433 700 $aLi$b Yinqin$01333094 702 $aYang$b Dachun$f1963- 702 $aHuang$b Long$c(Researcher of mathematics), 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996511863003316 996 $aReal-Variable Theory of Hardy Spaces Associated with Generalized Herz Spaces of Rafeiro and Samko$93371441 997 $aUNISA