Overview
- Presents a detailed and complete real-variable theory of generalized Herz-Hardy type function spaces
- Gives a fresh perspective of treating generalized Herz spaces as special cases of ball quasi-Banach function spaces
- Provides detailed and self-contained arguments for the new and sharp results
Part of the book series: Lecture Notes in Mathematics (LNM, volume 2320)
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Table of contents (8 chapters)
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Front Matter
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Back Matter
Keywords
- generalized Herz space
- ball quasi-Banach function space
- Hardy space
- localized Hardy space
- weak Hardy space
- atom
- molecule
- duality
- maximal function
- Littlewood-Paley function
- Hardy-Littlewood maximal operator
- Fefferman-Stein vector-valued inequality
- Calderon-Zygmund operator
- commutator
- pseudo-differential operator
About this book
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.
Authors and Affiliations
About the authors
Dachun Yang is a professor of mathematics at Beijing Normal University, China. He received his Ph.D. from Beijing Normal University in 1992 under the supervision of Shanzhen Lu. Since his Ph.D., real-variable theory about Herz–Hardy spaces has been one of Dachun Yang's research interests. His research interests now include real-variable theory of function spaces (associated with operators) on various underlying spaces including Euclidean spaces, metric measure spaces, and nonhomogeneous metric spaces, as well as their applications to the boundedness of (Riesz or singular integral) operators and multipliers. Dachun Yang and his co-authors have published 4 monographs and more than 400 journal articles.
Long Huang is a postdoctoral researcher of mathematics at Guangzhou University, China. He received his Ph. D. from Beijing Normal University in 2021 under the supervision of Dachun Yang. His research interests now include the real-variable theory of function spaces and its applications in the boundedness of operators.Bibliographic Information
Book Title: Real-Variable Theory of Hardy Spaces Associated with Generalized Herz Spaces of Rafeiro and Samko
Authors: Yinqin Li, Dachun Yang, Long Huang
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/978-981-19-6788-7
Publisher: Springer Singapore
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022
Softcover ISBN: 978-981-19-6787-0Published: 15 February 2023
eBook ISBN: 978-981-19-6788-7Published: 14 February 2023
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: XIX, 647
Number of Illustrations: 1 b/w illustrations
Topics: Several Complex Variables and Analytic Spaces, Fourier Analysis, Functional Analysis