Hardy Spaces On Homogeneous Groups
Download Hardy Spaces On Homogeneous Groups full books in PDF, epub, and Kindle. Read online free Hardy Spaces On Homogeneous Groups ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!
| Author | : Gerald B. Folland |
| Publisher | : Princeton University Press |
| Total Pages | : 302 |
| Release | : 2020-12-08 |
| Genre | : Mathematics |
| ISBN | : 0691222452 |
The object of this monograph is to give an exposition of the real-variable theory of Hardy spaces (HP spaces). This theory has attracted considerable attention in recent years because it led to a better understanding in Rn of such related topics as singular integrals, multiplier operators, maximal functions, and real-variable methods generally. Because of its fruitful development, a systematic exposition of some of the main parts of the theory is now desirable. In addition to this exposition, these notes contain a recasting of the theory in the more general setting where the underlying Rn is replaced by a homogeneous group. The justification for this wider scope comes from two sources: 1) the theory of semi-simple Lie groups and symmetric spaces, where such homogeneous groups arise naturally as "boundaries," and 2) certain classes of non-elliptic differential equations (in particular those connected with several complex variables), where the model cases occur on homogeneous groups. The example which has been most widely studied in recent years is that of the Heisenberg group.
| Author | : Michael Ruzhansky |
| Publisher | : Springer |
| Total Pages | : 579 |
| Release | : 2019-07-02 |
| Genre | : Mathematics |
| ISBN | : 303002895X |
This open access book provides an extensive treatment of Hardy inequalities and closely related topics from the point of view of Folland and Stein's homogeneous (Lie) groups. The place where Hardy inequalities and homogeneous groups meet is a beautiful area of mathematics with links to many other subjects. While describing the general theory of Hardy, Rellich, Caffarelli-Kohn-Nirenberg, Sobolev, and other inequalities in the setting of general homogeneous groups, the authors pay particular attention to the special class of stratified groups. In this environment, the theory of Hardy inequalities becomes intricately intertwined with the properties of sub-Laplacians and subelliptic partial differential equations. These topics constitute the core of this book and they are complemented by additional, closely related topics such as uncertainty principles, function spaces on homogeneous groups, the potential theory for stratified groups, and the potential theory for general Hörmander's sums of squares and their fundamental solutions. This monograph is the winner of the 2018 Ferran Sunyer i Balaguer Prize, a prestigious award for books of expository nature presenting the latest developments in an active area of research in mathematics. As can be attested as the winner of such an award, it is a vital contribution to literature of analysis not only because it presents a detailed account of the recent developments in the field, but also because the book is accessible to anyone with a basic level of understanding of analysis. Undergraduate and graduate students as well as researchers from any field of mathematical and physical sciences related to analysis involving functional inequalities or analysis of homogeneous groups will find the text beneficial to deepen their understanding.
| Author | : Gerald B. Folland |
| Publisher | : |
| Total Pages | : 284 |
| Release | : 1982 |
| Genre | : |
| ISBN | : |
| Author | : Gerald B. Folland |
| Publisher | : Princeton University Press |
| Total Pages | : 298 |
| Release | : 1982-06-21 |
| Genre | : Mathematics |
| ISBN | : 069108310X |
The object of this monograph is to give an exposition of the real-variable theory of Hardy spaces (HP spaces). This theory has attracted considerable attention in recent years because it led to a better understanding in Rn of such related topics as singular integrals, multiplier operators, maximal functions, and real-variable methods generally. Because of its fruitful development, a systematic exposition of some of the main parts of the theory is now desirable. In addition to this exposition, these notes contain a recasting of the theory in the more general setting where the underlying Rn is replaced by a homogeneous group. The justification for this wider scope comes from two sources: 1) the theory of semi-simple Lie groups and symmetric spaces, where such homogeneous groups arise naturally as "boundaries," and 2) certain classes of non-elliptic differential equations (in particular those connected with several complex variables), where the model cases occur on homogeneous groups. The example which has been most widely studied in recent years is that of the Heisenberg group.
| Author | : Marcin Bownik |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 136 |
| Release | : 2003 |
| Genre | : Mathematics |
| ISBN | : 082183326X |
Investigates the anisotropic Hardy spaces associated with very general discrete groups of dilations. This book includes the classical isotropic Hardy space theory of Fefferman and Stein and parabolic Hardy space theory of Calderon and Torchinsky.
| Author | : Ryan Alvarado |
| Publisher | : Springer |
| Total Pages | : 491 |
| Release | : 2015-06-09 |
| Genre | : Mathematics |
| ISBN | : 3319181327 |
Systematically constructing an optimal theory, this monograph develops and explores several approaches to Hardy spaces in the setting of Alhlfors-regular quasi-metric spaces. The text is divided into two main parts, with the first part providing atomic, molecular, and grand maximal function characterizations of Hardy spaces and formulates sharp versions of basic analytical tools for quasi-metric spaces, such as a Lebesgue differentiation theorem with minimal demands on the underlying measure, a maximally smooth approximation to the identity and a Calderon-Zygmund decomposition for distributions. These results are of independent interest. The second part establishes very general criteria guaranteeing that a linear operator acts continuously from a Hardy space into a topological vector space, emphasizing the role of the action of the operator on atoms. Applications include the solvability of the Dirichlet problem for elliptic systems in the upper-half space with boundary data from Hardy spaces. The tools established in the first part are then used to develop a sharp theory of Besov and Triebel-Lizorkin spaces in Ahlfors-regular quasi-metric spaces. The monograph is largely self-contained and is intended for mathematicians, graduate students and professionals with a mathematical background who are interested in the interplay between analysis and geometry.
| Author | : Mark Lʹvovich Agranovskiĭ |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 158 |
| Release | : 1993-01-01 |
| Genre | : Mathematics |
| ISBN | : 9780821897478 |
This book studies translation-invariant function spaces and algebras on homogeneous manifolds. The central topic is the relationship between the homogeneous structure of a manifold and the class of translation-invariant function spaces and algebras on the manifold. The author obtains classifications of translation-invariant spaces and algebras of functions on semisimple and nilpotent Lie groups, Riemann symmetric spaces, and bounded symmetric domains. When such classifications are possible, they lead in many cases to new characterizations of the classical function spaces, from the point of view of their group of admissible changes of variable. The algebra of holomorphic functions plays an essential role in these classifications when a homogeneous complex or $CR$-structure exists on the manifold. This leads to new characterizations of holomorphic functions and their boundary values for one- and multidimensional complex domains.
| Author | : Yinqin Li |
| Publisher | : Springer Nature |
| Total Pages | : 663 |
| Release | : 2023-02-14 |
| Genre | : Mathematics |
| ISBN | : 9811967881 |
The 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.
| Author | : Dachun Yang |
| Publisher | : Springer |
| Total Pages | : 476 |
| Release | : 2017-05-09 |
| Genre | : Mathematics |
| ISBN | : 331954361X |
The main purpose of this book is to give a detailed and complete survey of recent progress related to the real-variable theory of Musielak–Orlicz Hardy-type function spaces, and to lay the foundations for further applications. The real-variable theory of function spaces has always been at the core of harmonic analysis. Recently, motivated by certain questions in analysis, some more general Musielak–Orlicz Hardy-type function spaces were introduced. These spaces are defined via growth functions which may vary in both the spatial variable and the growth variable. By selecting special growth functions, the resulting spaces may have subtler and finer structures, which are necessary in order to solve various endpoint or sharp problems. This book is written for graduate students and researchers interested in function spaces and, in particular, Hardy-type spaces.
| Author | : Shanzhen Lu |
| Publisher | : World Scientific |
| Total Pages | : 236 |
| Release | : 1995 |
| Genre | : Mathematics |
| ISBN | : 9789810221584 |
This book introduces the real variable theory of HP spaces briefly and concentrates on its applications to various aspects of analysis fields. It consists of four chapters. Chapter 1 introduces the basic theory of Fefferman-Stein on real HP spaces. Chapter 2 describes the atomic decomposition theory and the molecular decomposition theory of real HP spaces. In addition, the dual spaces of real HP spaces, the interpolation of operators in HP spaces, and the interpolation of HP spaces are also discussed in Chapter 2. The properties of several basic operators in HP spaces are discussed in Chapter 3 in detail. Among them, some basic results are contributed by Chinese mathematicians, such as the decomposition theory of weak HP spaces and its applications to the study on the sharpness of singular integrals, a new method to deal with the elliptic Riesz means in HP spaces, and the transference theorem of HP-multipliers etc. The last chapter is devoted to applications of real HP spaces to approximation theory.
