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1、SingularIntegralsandRelatedTopicsThispageintentionallyleftblankSingularIntegralsandRelatedTopicsShanzhenLuYongDingBeijingNormalUniversity,ChinaDunyanYanAcademiaSinica,ChinaWorldScientificNEWJERSEY•LONDON•SINGAPORE•BEIJING•SHANGHAI•HONGKONG•TAIPEI•CHENNA
2、IPublishedbyWorldScientificPublishingCo.Pte.Ltd.5TohTuckLink,Singapore596224USAoffice:27WarrenStreet,Suite401-402,Hackensack,NJ07601UKoffice:57SheltonStreet,CoventGarden,LondonWC2H9HEBritishLibraryCataloguing-in-PublicationDataAcataloguerecordforthisboo
3、kisavailablefromtheBritishLibrary.SINGULARINTEGRALSANDRELATEDTOPICSCopyright©2007byWorldScientificPublishingCo.Pte.Ltd.Allrightsreserved.Thisbook,orpartsthereof,maynotbereproducedinanyformorbyanymeans,electronicormechanical,includingphotocopying,recordi
4、ngoranyinformationstorageandretrievalsystemnowknownortobeinvented,withoutwrittenpermissionfromthePublisher.Forphotocopyingofmaterialinthisvolume,pleasepayacopyingfeethroughtheCopyrightClearanceCenter,Inc.,222RosewoodDrive,Danvers,MA01923,USA.Inthiscasep
5、ermissiontophotocopyisnotrequiredfromthepublisher.ISBN-13978-981-270-623-2ISBN-10981-270-623-2PrintedinSingapore.ZhangJi-SingularIntegrals.pmd16/4/2007,12:15PMPrefaceItiswell-knownthatsingularintegralsiscontinuouslyregardedasacentralroleinharmonicanalys
6、is.Therearemanynicebooksrelatedtosingularintegrals.Inthisbook,thereareatleasttwosideswhichdi erfromtheotherbooks.Oneofthemistoestablishmoreperfecttheoryofsingularintegrals.Itincludesnotonlythecaseofsmoothkernels,butalsothecaseofroughkernels.Inthesameway
7、,wedealwithsomerelatedoperators,suchasfractionalintegraloperatorsandLittlewood-Paleyoperators.Theotheristointroducemorenewtheoryonsomeoscillatorysingularintegralswithpolynomialphases.Thisbookismainlyprovidedtograduatestudentsinanalysis eld.However,itisa
8、lsobene cialtoresearchersinmathematics.Thisbookconsistsof vechapters.Letusnowillustratethechoiceofmaterialineachchapter.Chapter1isdevotedtothetheoryoftheHardy-Littlewoodmaximaloperatorasthebasisofsingularintegralsandotherrelatedo
