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Author : Guozhen Lu
Publisher : American Mathematical Society
Page : 100 pages
File Size : 14,41 MB
Release : 2023-01-18
Category : Mathematics
ISBN : 1470455374
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Author : Jiawei Shen
Publisher :
Page : 119 pages
File Size : 41,21 MB
Release : 2018
Category : Mathematics
ISBN :
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 : Kannan Soundararajan
Publisher : American Mathematical Society
Page : 100 pages
File Size : 29,41 MB
Release : 2022-11-09
Category : Mathematics
ISBN : 1470469308
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 : Brian Street
Publisher : Princeton University Press
Page : 411 pages
File Size : 34,11 MB
Release : 2014-10-05
Category : Mathematics
ISBN : 0691162522
This book develops a new theory of multi-parameter singular integrals associated with Carnot-Carathéodory balls. Brian Street first details the classical theory of Calderón-Zygmund singular integrals and applications to linear partial differential equations. He then outlines the theory of multi-parameter Carnot-Carathéodory geometry, where the main tool is a quantitative version of the classical theorem of Frobenius. Street then gives several examples of multi-parameter singular integrals arising naturally in various problems. The final chapter of the book develops a general theory of singular integrals that generalizes and unifies these examples. This is one of the first general theories of multi-parameter singular integrals that goes beyond the product theory of singular integrals and their analogs. Multi-parameter Singular Integrals will interest graduate students and researchers working in singular integrals and related fields.
Author : Tarek M. Elgindi
Publisher : American Mathematical Society
Page : 102 pages
File Size : 20,76 MB
Release : 2023-03-09
Category : Mathematics
ISBN : 1470456826
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Author : Nassif Ghoussoub
Publisher : American Mathematical Society
Page : 138 pages
File Size : 32,76 MB
Release : 2023-05-23
Category : Mathematics
ISBN : 1470461196
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Author : Martin Herschend
Publisher : American Mathematical Society
Page : 156 pages
File Size : 38,63 MB
Release : 2023-05-23
Category : Mathematics
ISBN : 1470456311
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Author : Björn Sandstede
Publisher : American Mathematical Society
Page : 116 pages
File Size : 24,42 MB
Release : 2023-05-23
Category : Mathematics
ISBN : 1470463091
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Author : Sema Güntürkün
Publisher : American Mathematical Society
Page : 148 pages
File Size : 42,32 MB
Release : 2023-06-22
Category : Mathematics
ISBN : 1470465469
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Author : Yi Huang
Publisher : American Mathematical Society
Page : 128 pages
File Size : 19,83 MB
Release : 2023-06-22
Category : Mathematics
ISBN : 1470463121
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