欧几里得空间的傅立叶分析

图书标准信息

• 作者 [美]斯德恩 著
• 出版社 世界图书出版公司
• 出版时间 2009-08
• 版次 1
• ISBN 9787510005329
• 定价 46.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 297页
• 正文语种 英语

【内容简介】

 This book is designed to be an introduction to harmonic analysis inEuclidean spaces. The subject has seen a considerable flowering during thepast twenty years. We have not tried to cover all phases of this develop-ment. Rather, our chief concern was to illustrate various methods used inthis aspect of Fourier analysis that exploit the structure of Euclideanspaces. In particular, we try to show the role played by the action oftranslations, dilations, and rotations. Another concern, not independentof this chief one, is to motivate the study of harmonic analysis on moregeneral spaces having an analogous structure （such as arises in symmetricspaces）. It is our feeling that the study of Fourier analysis in that contextand, also, in other general settings, is more meaningful once the specialEuclidean case is understood.

【目录】

Preface

CHAPTERⅠTheFourierTransform

1.ThebasicL1theoryoftheFouriertransform

2.TheL2theoryandthePlanchereltheorem

3.Theclassoftempereddistributions

4.Furtherresults

CHAPTERⅡBoundaryValuesofHarmonicFunctions

1.Basicpropertiesofharmonicfunctions

2.ThecharacterizationofPoissonintegrals

3.TheHardy-Littlewoodmaximalfunctionandnontangentialconvergenceofharmonicfunctions

4.Subharmonicfunctionsandmajorizationbyharmonicfunctions

5.Furtherresults

CHAPTERⅢTheTheoryofHpSpacesonTubes

1.Introductoryremarks

2.TheH2theory

3.Tubesovercones

4.ThePaley-Wienertheorem

5.TheHptheory

6.Furtherresults

CHAPTERⅣSymmetryPropertiesoftheFourierTransform

1.DecompositionofL2(Ez)intosub，pacesinvariantundertheFouriertransform

2.Sphericalharmonics

3.TheactionoftheFouriertransformonthespaces

4.Someapplications

5.Furtherresults

CHAPTERⅤInterpolationofOperators

1.TheM.RieszconvexitytheoremandinterpolationofoperatorsdefinedonLpspaces

2.TheMarcinkiewiczinterpolationtheorem

3.L(p，q)spaces

4.Interpolationofanalyticfamiliesofoperators

5.Furtherresults

CHAPTERⅥSingularIntegralsandSystemsofConjugateHarmonicFunctions

1.TheHilberttransform

2.Singularintegraloperatorswithoddkernels

3.Singularintegraloperatorswithevenkernels

4.Hpspacesofconjugateharmonicfunctions

5.Furtherresults

CHAPTERⅦMultipleFourierSeries

1.Elementaryproperties

2.ThePoissonsummationformula

3.Multipliertransformations

4.Summabilitybelowthecriticalindex(negativeresults)

5.Summabilitybelowthecriticalindex

6.Furtherresults

Bibliography

Index