Real-Variable Theory of Hardy Spaces Associated with Generalized Herz Spaces of Rafeiro and Samko

Description

Preface Abstract Keywords and Phrases Contents 1 Generalized Herz Spaces of Rafeiro and Samko 1.1 Matuszewska–Orlicz Indices 1.2 Generalized Herz Spaces 1.3 Convexities 1.4 Absolutely Continuous Quasi-Norms 1.5 Boundedness of Sublinear Operators 1.6 Fefferman–Stein Vector-Valued Inequalities 1.7 Dual and Associate Spaces of Local Generalized Herz Spaces 1.8 Extrapolation Theorems 2 Block Spaces and Their Applications 2.1 Block Spaces 2.2 Duality 2.3 Boundedness of Sublinear Operators 3 Boundedness and Compactness Characterizations of Commutators on Generalized Herz Spaces 3.1 Boundedness Characterizations 3.2 Compactness Characterizations 4 Generalized Herz–Hardy Spaces 4.1 Maximal Function Characterizations 4.2 Relations with Generalized Herz Spaces 4.3 Atomic Characterizations 4.4 Generalized Finite Atomic Herz–Hardy Spaces 4.5 Molecular Characterizations 4.6 Littlewood–Paley Function Characterizations 4.7 Dual Space of Hω,0p,q(Rn) 4.8 Boundedness of Calderón–Zygmund Operators 4.9 Fourier Transform 5 Localized Generalized Herz–Hardy Spaces 5.1 Maximal Function Characterizations 5.2 Relations with Generalized Herz–Hardy Spaces 5.3 Atomic Characterizations 5.4 Molecular Characterizations 5.5 Littlewood–Paley Function Characterizations 5.6 Boundedness of Pseudo-Differential Operators 6 Weak Generalized Herz–Hardy Spaces 6.1 Maximal Function Characterizations 6.2 Relations with Weak Generalized Herz Spaces 6.3 Atomic Characterizations 6.4 Molecular Characterizations 6.5 Littlewood–Paley Function Characterizations 6.6 Boundedness of Calderón–Zygmund Operators 6.7 Real Interpolations 7 Inhomogeneous Generalized Herz Spaces and Inhomogeneous Block Spaces 7.1 Inhomogeneous Generalized Herz Spaces 7.1.1 Convexities 7.1.2 Absolutely Continuous Quasi-Norms 7.1.3 Boundedness of Sublinear Operators and Fefferman–Stein Vector-Valued Inequalities 7.1.4 Dual and Associate Spaces of Inhomogeneous Local Generalized Herz Spaces 7.1.5 Extrapolation Theorems 7.2 Inhomogeneous Block Spaces and Their Applications 7.2.1 Inhomogeneous Block Spaces 7.2.2 Duality Between Inhomogeneous Block Spaces and Global Generalized Herz Spaces 7.2.3 Boundedness of Sublinear Operators 7.3 Boundedness and Compactness Characterizations of Commutators 7.3.1 Boundedness Characterizations 7.3.2 Compactness Characterizations 8 Hardy Spaces Associated with Inhomogeneous Generalized Herz Spaces 8.1 Inhomogeneous Generalized Herz–Hardy Spaces 8.1.1 Maximal Function Characterizations 8.1.2 Relations with Inhomogeneous Generalized Herz Spaces 8.1.3 Atomic Characterizations 8.1.4 Inhomogeneous Generalized Finite Atomic Herz–Hardy Spaces 8.1.5 Molecular Characterizations 8.1.6 Littlewood–Paley Function Characterizations 8.1.7 Dual Space of HKω,0p,q(Rn) 8.1.8 Boundedness of Calderón–Zygmund Operators 8.1.9 Fourier Transform 8.2 Inhomogeneous Localized Generalized Herz–Hardy Spaces 8.2.1 Maximal Function Characterizations 8.2.2 Relations with Inhomogeneous Generalized Herz–Hardy Spaces 8.2.3 Atomic Characterizations 8.2.4 Molecular Characterizations 8.2.5 Littlewood–Paley Function Characterizations 8.2.6 Boundedness of Pseudo-Differential Operators 8.3 Inhomogeneous Weak Generalized Herz–Hardy Spaces 8.3.1 Maximal Function Characterizations 8.3.2 Relations with Inhomogeneous Weak Generalized Herz Spaces 8.3.3 Atomic Characterizations 8.3.4 Molecular Characterizations 8.3.5 Littlewood–Paley Function Characterizations 8.3.6 Boundedness of Calderón–Zygmund Operators 8.3.7 Real Interpolations Bibliography Index