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

The real-variable theory of function spaces is a fundamental tool of harmonic analysis, and this book explores properties of generalized Herz spaces and establishes a complete real-variable theory of Hardy spaces associated with local and global generalized Herz spaces via a fresh perspective. It also establishes the boundedness of some important operators arising from harmonic analysis on these Herz–Hardy spaces and investigates inhomogeneous Herz–Hardy spaces.

Format: Paperback / softback
Length: 647 pages
Publication date: 15 February 2023
Publisher: Springer Verlag, Singapore

The real-variable theory of function spaces has played a central role in harmonic analysis, particularly in the realm of the Hardy space. In particular, the real-variable theory of the Hardy space stands as a fundamental tool in harmonic analysis, with applications and connections to complex analysis, partial differential equations, and functional analysis.

This book is dedicated to delving into the properties of generalized Herz spaces and establishing a comprehensive real-variable theory of Hardy spaces, particularly in the context of local and global generalized Herz spaces. The authors approach these generalized Herz spaces as special cases of ball quasi-Banach function spaces, offering a fresh perspective on their study.

In the first part of the book, the authors introduce some fundamental properties of generalized Herz spaces and derive boundedness and compactness characterizations for commutators on these spaces. They then introduce associated Herz–Hardy spaces, localized Herz–Hardy spaces, and weak Herz–Hardy spaces, and develop a complete real-variable theory for these spaces. This theory encompasses various maximal function, atomic, molecular, and Littlewood–Paley function characterizations. As applications, the authors establish the boundedness of certain operators arising from harmonic analysis on these Herz–Hardy spaces.

Furthermore, the book explores inhomogeneous Herz–Hardy spaces and their complete real-variable theory. By adopting the fresh perspective and achieving improved conclusions on the real-variable theory of Hardy spaces associated with ball quasi-Banach function spaces, the obtained results in this book are novel, and their related exponents are sharp. This book will be of interest to researchers and graduate students who are passionate about function spaces and their applications.

Weight: 1015g
Dimension: 235 x 155 (mm)
ISBN-13: 9789811967870
Edition number: 1st ed. 2022