Hardy Space Theory and Endpoint Estimates for Multi-parameter Singular Radon Transforms PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Hardy Space Theory and Endpoint Estimates for Multi-parameter Singular Radon Transforms PDF full book. Access full book title Hardy Space Theory and Endpoint Estimates for Multi-parameter Singular Radon Transforms by Jiawei Shen. Download full books in PDF and EPUB format.
Author: Jiawei Shen
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 119
Get Book Here
Book Description
In [12], Christ, Nagel, Stein and Waigner studied the L p theories for the singular Radon Trans- forms. Furthermore, B. Street in [68], and Stein and Street in [640́367] extended the theories of the L p boundedness for multi-parameter singular integral operators, such as the Calder©đn Zygmund operators and singular Radon transforms. In this dissertation, we will study the Hardy space H p and its dual space associated with both the one-parameter and multi-parameter singular Radon transforms, and consider the boundedness of the singular Radon transforms on such Hardy spaces H p when 0 9́Þ p 9́Þ 1. Inspired by recent characterization of the Hardy spaces on product spaces, we will take advan- tage of the discrete Littlewood-Paley analysis [14,32,43] to define the Hardy spaces H p and the Carleson measure spaces CMO p associated with the multi-parameter singular Radon transforms. Moreover, we will prove the H p boundedness of those operators and thus obtain the endpoint es- timates for the L p boundedness of the singular Radon transforms by Christ, Nagel, Wainger and Stein [12] and and for multi-parameter singular Radon transforms by Street and Stein [650́368].
Author: Jiawei Shen
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 119
Get Book Here
Book Description
In [12], Christ, Nagel, Stein and Waigner studied the L p theories for the singular Radon Trans- forms. Furthermore, B. Street in [68], and Stein and Street in [640́367] extended the theories of the L p boundedness for multi-parameter singular integral operators, such as the Calder©đn Zygmund operators and singular Radon transforms. In this dissertation, we will study the Hardy space H p and its dual space associated with both the one-parameter and multi-parameter singular Radon transforms, and consider the boundedness of the singular Radon transforms on such Hardy spaces H p when 0 9́Þ p 9́Þ 1. Inspired by recent characterization of the Hardy spaces on product spaces, we will take advan- tage of the discrete Littlewood-Paley analysis [14,32,43] to define the Hardy spaces H p and the Carleson measure spaces CMO p associated with the multi-parameter singular Radon transforms. Moreover, we will prove the H p boundedness of those operators and thus obtain the endpoint es- timates for the L p boundedness of the singular Radon transforms by Christ, Nagel, Wainger and Stein [12] and and for multi-parameter singular Radon transforms by Street and Stein [650́368].
Author: GUOZHEN;SHEN LU (JIAWEI;ZHANG, LU.)
Publisher:
ISBN: 9781470473211
Category :
Languages : en
Pages : 0
Get Book Here
Book Description
Author: Guozhen Lu
Publisher: American Mathematical Society
ISBN: 1470455374
Category : Mathematics
Languages : en
Pages : 100
Get Book Here
Book Description
View the abstract.
Author: Kannan Soundararajan
Publisher: American Mathematical Society
ISBN: 1470469308
Category : Mathematics
Languages : en
Pages : 100
Get Book Here
Book Description
This book uses finite field theory as a hook to introduce the reader to a range of ideas from algebra and number theory. It constructs all finite fields from scratch and shows that they are unique up to isomorphism. As a payoff, several combinatorial applications of finite fields are given: Sidon sets and perfect difference sets, de Bruijn sequences and a magic trick of Persi Diaconis, and the polynomial time algorithm for primality testing due to Agrawal, Kayal and Saxena. The book forms the basis for a one term intensive course with students meeting weekly for multiple lectures and a discussion session. Readers can expect to develop familiarity with ideas in algebra (groups, rings and fields), and elementary number theory, which would help with later classes where these are developed in greater detail. And they will enjoy seeing the AKS primality test application tying together the many disparate topics from the book. The pre-requisites for reading this book are minimal: familiarity with proof writing, some linear algebra, and one variable calculus is assumed. This book is aimed at incoming undergraduate students with a strong interest in mathematics or computer science.
Author: Lingxiao Zhang (Ph.D.)
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
Get Book Here
Book Description
We study operators of the formTf(x)= \psi(x) \int f(\gamma_t(x))K(t)\,dt, where \gamma_t(x) is a real analytic function of (t,x) mapping from a neighborhood of (0,0) in \mathbb{R}^N \times \mathbb{R}^n into \mathbb{R}^n satisfying \gamma_0(x)\equiv x, \psi(x) \in C_c^\infty(\mathbb{R}^n), and K(t) is a ``multi-parameter singular kernel'' with compact support in \mathbb{R}^N; for example when K(t) is a product singular kernel. The celebrated work of Christ, Nagel, Stein, and Wainger studied such operators with smooth \gamma_t(x), in the single-parameter case when K(t) is a Calder\'on-Zygmund kernel. Street and Stein generalized their work to the multi-parameter case, and gave sufficient conditions for the L^p-boundedness of such operators. This paper shows that when \gamma_t(x) is real analytic, the sufficient conditions of Street and Stein are also necessary for the L^p-boundedness of T, for all such kernels K.
Author: Lingxiao Zhang (Ph.D.)
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
Get Book Here
Book Description
We study operators of the formTf(x)= \psi(x) \int f(\gamma_t(x))K(t)\,dt, where \gamma_t(x) is a real analytic function of (t,x) mapping from a neighborhood of (0,0) in \mathbb{R}^N \times \mathbb{R}^n into \mathbb{R}^n satisfying \gamma_0(x)\equiv x, \psi(x) \in C_c^\infty(\mathbb{R}^n), and K(t) is a ``multi-parameter singular kernel'' with compact support in \mathbb{R}^N; for example when K(t) is a product singular kernel. The celebrated work of Christ, Nagel, Stein, and Wainger studied such operators with smooth \gamma_t(x), in the single-parameter case when K(t) is a Calder\'on-Zygmund kernel. Street and Stein generalized their work to the multi-parameter case, and gave sufficient conditions for the L^p-boundedness of such operators. This paper shows that when \gamma_t(x) is real analytic, the sufficient conditions of Street and Stein are also necessary for the L^p-boundedness of T, for all such kernels K.
Author: Terence Tao
Publisher: American Mathematical Soc.
ISBN: 1470466406
Category : Education
Languages : en
Pages : 206
Get Book Here
Book Description
This is a graduate text introducing the fundamentals of measure theory and integration theory, which is the foundation of modern real analysis. The text focuses first on the concrete setting of Lebesgue measure and the Lebesgue integral (which in turn is motivated by the more classical concepts of Jordan measure and the Riemann integral), before moving on to abstract measure and integration theory, including the standard convergence theorems, Fubini's theorem, and the Carathéodory extension theorem. Classical differentiation theorems, such as the Lebesgue and Rademacher differentiation theorems, are also covered, as are connections with probability theory. The material is intended to cover a quarter or semester's worth of material for a first graduate course in real analysis. There is an emphasis in the text on tying together the abstract and the concrete sides of the subject, using the latter to illustrate and motivate the former. The central role of key principles (such as Littlewood's three principles) as providing guiding intuition to the subject is also emphasized. There are a large number of exercises throughout that develop key aspects of the theory, and are thus an integral component of the text. As a supplementary section, a discussion of general problem-solving strategies in analysis is also given. The last three sections discuss optional topics related to the main matter of the book.
Author: Steven G. Krantz
Publisher: Springer Science & Business Media
ISBN: 0817646698
Category : Mathematics
Languages : en
Pages : 367
Get Book Here
Book Description
This self-contained text provides an introduction to modern harmonic analysis in the context in which it is actually applied, in particular, through complex function theory and partial differential equations. It takes the novice mathematical reader from the rudiments of harmonic analysis (Fourier series) to the Fourier transform, pseudodifferential operators, and finally to Heisenberg analysis.
Author: Andreas Seeger
Publisher: American Mathematical Soc.
ISBN: 1470434377
Category : Forms (Mathematics)
Languages : en
Pages : 142
Get Book Here
Book Description
Author:
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 964
Get Book Here
Book Description
