奇异积分和函数的可微性（英文） [Singular Integrals and Diffferentiability Properties of Functions] pdf epub mobi txt 电子书 下载 2025

简体网页||繁体网页

☆☆☆☆☆

施泰恩（Stein E.M.） 著

承接 住宅 自建房 室内改造 装修设计 免费咨询 QQ：624617358 一级注册建筑师 亲自为您回答、经验丰富，价格亲民。无论项目大小，都全力服务。期待合作，欢迎咨询！QQ：624617358

出版社： 世界图书出版公司

ISBN：9787510035135

版次：1

商品编码：10891446

包装：平装

外文名称：Singular Integrals and Diffferentiability Properties of Functions

开本：24开

出版时间：2011-06-01

页数：287

正文语种：英文

内容简介

This book is an outgrowth of a course which I gave at Orsay duringthe academic year 1 966.67 MY purpose in those lectures was to pre-sent some of the required background and at the same time clarify theessential unity that exists between several related areas of analysis.These areas are：the existence and boundedness of singular integral op-erators；the boundary behavior of harmonic functions；and differentia-bility properties of functions of several variables.AS such the commoncore of these topics may be said to represent one of the central develop-ments in n.dimensional Fourier analysis during the last twenty years，and it can be expected to have equal influence in the future.These pos.

作者简介

作者：(美国)施泰恩(SteinE.M.)

内页插图

目录

PREFACE
NOTATION
I．SOME FUNDAMENTAL NOTIONS OF REAL．VARIABLE THEORY
The maximal function
Behavior near general points of measurable sets
Decomposition in cubes of open sets in R”
An interpolation theorem for L
Further results

II．SINGULAR INTEGRALS
Review of certain aspects of harmonic analysis in R”
Singular integrals：the heart of the matter
Singular integrals：some extensions and variants of the
preceding
Singular integral operaters which commute with dilations
Vector．valued analogues
Further results

III．RIESZ TRANSFORMS，POLSSON INTEGRALS，AND SPHERICAI HARMONICS
The Riesz transforms
Poisson integrals and approximations to the identity
Higher Riesz transforms and spherical harmonics
Further results

IV．THE LITTLEWOOD．PALEY THEORY AND MULTIPLIERS
The Littlewood-Paley g-function
The functiong
Multipliers（first version）
Application of the partial sums operators
The dyadic decomposition
The Marcinkiewicz multiplier theorem
Further results

V．DIFFERENTIABlLITY PROPERTIES IN TERMS OF FUNCTION SPACES
Riesz potentials
The Sobolev spaces
BesseI potentials
The spaces of Lipschitz continuous functions
The spaces
Further results

VI．EXTENSIONS AND RESTRICTIONS
Decomposition of open sets into cubes
Extension theorems of Whitney type
Extension theorem for a domain with minimally smooth
boundary
Further results

VII．RETURN TO THE THEORY OF HARMONIC FUNCTIONS
Non-tangential convergence and Fatou'S theorem
The area integral
Application of the theory of H”spaces
Further results

VIII．DIFFERENTIATION OF FUNCTIONS
Several qotions of pointwise difierentiability
The splitting of functions
A characterization 0f difrerentiability
Desymmetrization principle
Another characterization of difirerentiabiliW
Further results
APPENDICES
Some Inequalities
The Marcinkiewicz Interpolation Theorem
Some Elementary Properties of Harmonic Functions
Inequalities for Rademacher Functions
BlBLl0GRAPHY
INDEX

精彩书摘

The basic ideas of the theory of reaI variables are connected with theconcepts of sets and ftmctions，together with the processes of integrationand difirerentiation applied to them.WhiIe the essential aspects of theseideas were brought to light in the early part of our century，some of theirfurther applications were developed only more recently.It iS from thislatter perspective that we shall approach that part of the theory thatinterests US.In doing SO，we distinguish several main features： The theorem of Lebesgue about the differentiation of the integral.The study of properties related to this process iS best done in terms of a“maximal function”to which it gives rise：the basic features of the latterare expressed in terms of a“weak-type”inequality which iS characteristicof this situation. Certain covering lemmas.In general the idea iS to cover an arbitraryopen set in terms of a disioint union ofcubes or balls，chosen in a mannerdepending on the problem at hand.ORe such example iS a lemma ofWhitney，fTheorem 3）.Sometimes，however，it SHffices to cover only aportion of the set。as in the simple covering lemma，which iS used to provethe weak-type inequality mentioned above. f31 Behavior near a‘'general”point of an arbitrary set.The simplest notion here iS that of point of density.More refined properties are bestexpressed in terms of certain integrals first studied systematically by Marcinkiewicz.
（4）The splitting of functions into their large and small parts.Thisfeature which iS more of a technique than an end in itself，recurs often.ItiS especially useful in proving Linequalities，as in the first theorem ofthis chapter.That part of the proof of the first theorem iS systematizedin the Marcinkiewicz interpolation theorem discussed in§4 of this chapter and also in Appendix B.
......

前言/序言

评分☆☆☆☆☆

斯坦福分析系列，很好的书，京东送货快！

评分☆☆☆☆☆

还没看，先给个好评吧。物流也快。好评。

评分☆☆☆☆☆

张美丽在我的心中变得栩栩如生却又面目模糊。在过滤掉众多信息之后，唯一烙印在我们这群学生心中的是，据说“张美丽长得好像月历上，那些靠着摩托车摆姿势的女郎”。

评分☆☆☆☆☆

但小镇没预料到的是，与妖魔化同时进行的，是神化。

评分☆☆☆☆☆

Stein大师著名的调和三部曲之一，买来学习观摩

评分☆☆☆☆☆

大师作品，可供扩大知识面

评分☆☆☆☆☆

作为实变的后续学习文本，Stein是最好的选择了吧？这书接上一本傅里叶分析，下接调和分析。Stein作为陶哲轩的老师，其书观点新颖，处理问题别具特色，是难得的好书。

评分☆☆☆☆☆

调和分析入门的好书

评分☆☆☆☆☆

据说，她本来是个乖巧美丽的女人；据说，她喜欢上一个跟着轮船来这里进货的外地男人：据说，那男人长得身材魁梧，好打抱不平。在这个小镇，结婚前女人不能破身，她却私自把自己给了那男人。他们曾想私奔，最终被拦下，张美丽因而自杀。