Harmonic analysis, partial differential equations, banach spaces, and Operator Theory (Volume 2) : celebrating Cora Sadosky's life PDF
Preview Harmonic analysis, partial differential equations, banach spaces, and Operator Theory (Volume 2) : celebrating Cora Sadosky's life
Association for Women in Mathematics Series María Cristina Pereyra Stefania Marcantognini Alexander M. Stokolos Wilfredo Urbina Editors Harmonic Analysis, Partial Differential Equations, Banach Spaces, and Operator Theory (Volume 2) Celebrating Cora Sadosky's Life Association for Women in Mathematics Series Volume 5 SeriesEditor KristinLauter MicrosoftResearch Redmond,Washington,USA Moreinformationaboutthisseriesathttp://www.springer.com/series/13764 Association for Women in Mathematics Series Focusingonthegroundbreakingworkofwomeninmathematicspast,present,and future,Springer’sAssociationforWomeninMathematicsSeriespresentsthelatest research and proceedings of conferences worldwide organized by the Association forWomeninMathematics(AWM).Allworksarepeer-reviewedtomeetthehighest standardsofscientificliterature,whilepresentingtopicsatthecuttingedgeofpure andappliedmathematics.Sinceitsinceptionin1971,TheAssociationforWomenin Mathematicshasbeenanon-profitorganizationdesignedtohelpencouragewomen and girls to study and pursue active careers in mathematics and the mathematical sciencesandtopromoteequalopportunityandequaltreatmentofwomenandgirls inthemathematicalsciences.Currently,theorganizationrepresentsmorethan3000 members and 200 institutions constituting a broad spectrum of the mathematical community,intheUnitedStatesandaroundtheworld. María Cristina Pereyra (cid:129) Stefania Marcantognini Alexander M. Stokolos (cid:129) Wilfredo Urbina Editors Harmonic Analysis, Partial Differential Equations, Banach Spaces, and Operator Theory (Volume 2) Celebrating Cora Sadosky’s Life 123 Editors MaríaCristinaPereyra StefaniaMarcantognini DepartmentofMathematicsandStatistics DepartmentofMathematics UniversityofNewMexico VenezuelanInstituteforScientificResearch Albuquerque,NM,USA Caracas,Venezuela AlexanderM.Stokolos WilfredoUrbina DepartmentofMathematicalSciences DepartmentofMathematical GeorgiaSouthernUniversity andActuarialSciences Statesboro,GA,USA RooseveltUniversityChicago Chicago,IL,USA ISSN2364-5733 ISSN2364-5741 (electronic) AssociationforWomeninMathematicsSeries ISBN978-3-319-51591-5 ISBN978-3-319-51593-9 (eBook) DOI10.1007/978-3-319-51593-9 LibraryofCongressControlNumber:2016946423 ©TheAuthor(s)andtheAssociationforWomeninMathematics2017 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof thematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation, broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology nowknownorhereafterdeveloped. Theuseofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc.inthispublication doesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevant protectivelawsandregulationsandthereforefreeforgeneraluse. Thepublisher,theauthorsandtheeditorsaresafetoassumethattheadviceandinformationinthisbook arebelievedtobetrueandaccurateatthedateofpublication.Neitherthepublishernortheauthorsor theeditorsgiveawarranty,expressorimplied,withrespecttothematerialcontainedhereinorforany errorsoromissionsthatmayhavebeenmade.Thepublisherremainsneutralwithregardtojurisdictional claimsinpublishedmapsandinstitutionalaffiliations. Printedonacid-freepaper ThisSpringerimprintispublishedbySpringerNature TheregisteredcompanyisSpringerInternationalPublishingAG Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland v PhotographbyMargaretRandall,February2,2004 Preface for Volume 2 OnApril4,2014,wecelebratedCoraSadosky’slifewithanafternooninherhonor, preceded by the 13th New Mexico Analysis Seminar1 on April 3–4, 2014, and followed by the Western Sectional Meeting of the AMS on April 5–6, 2014, all held in Albuquerque, New Mexico, USA. It was a mathematical feast, gathering more than a hundred analysts – fledgling, junior and senior – from all over the USAandtheworldsuchasCanada,India,Mexico,Sweden,theUK,SouthKorea, Brazil,Israel,Hungary,Finland,Australia,Venezuela,andSpain,torememberher outspokenness,heruncompromisingways,hersharpsenseofhumor,hererudition, andaboveallherprofoundloveformathematics. Many speakers talked about how their mathematical lives were influenced by Cora’s magnetic personality and her mentoring early in their careers and as they grew into independent mathematicians. Particularly felt was her influence among young Argentinian and Venezuelan mathematicians. Rodolfo Torres, in a splendid lecture about Cora and her mathematics, transported us through the years from Buenos Aires to Chicago back to Buenos Aires, from Caracas to the USA back toBuenosAires,andfromWashingtonD.C.toCalifornia.HeremindedusofCora alwaysstandingupforhumanrights,CorapresidentoftheAssociationforWomen in Mathematics (AWM), and Cora always encouraging and fighting for what she thoughtwasright. 1The 13th New Mexico Analysis Seminar and An Afternoon in Honor of Cora Sadosky were sponsoredbyNationalScienceFoundation(NSF)GrantDMS-140042,theSimonsFoundation, andtheEfroymsonFoundation,andtheeventsweredoneincooperationwiththeAssociationfor WomeninMathematics(AWM).Seetheconferenceswebsites: www.math.unm.edu/conferences/13thAnalysis people.math.umass.edu/~nahmod/CoraSadosky.html AnAfternooninHonorofCoraSadoskywasorganizedbyAndreaNahmod,CristinaPereyra, andWilfredoUrbina.The13thNewMexicoAnalysisSeminarorganizerswereMattBlair,Cristina Pereyra, Anna Skripka, and Maxim Zinchenko from the University of New Mexico and Nick MichalowskifromNewMexicoStateUniversity. vii viii PrefaceforVolume2 Cora was born in Buenos Aires, Argentina, on May 23, 1940, and died on December3,2010,inLongBeach,CA.CoragotherPhDin1965attheUniversity ofChicagounderthesupervisionofbothAlbertoCalderónandAnthoniZygmund, the grandparents of the now-known Calderón-Zygmund School. Shortly after her return from Chicago, she married Daniel J. Goldstein, her lifelong companion who sadly passed away on March 13, 2014, a few weeks before the Albuquerque gathering.DanielandCorahadadaughter,CoraSol,whoisnowapoliticalscience professoratCaliforniaStateUniversityinLongBeach,andagranddaughter,Sasha Malena, who brightened their last years. During her life, Cora wrote more than 50 research papers, a graduate textbook (Interpolation of Operators and Singular Integrals: An Introduction to Harmonic Analysis, Marcel Dekker 1979), and she edited two volumes: one celebrating Mischa Cotlar’s 70th birthday (Analysis and PartialDifferentialEquations:ACollectionofPapersDedicatedtoMischaCotlar, CRCPress,1989)andonecelebratingAlbertoCalderón’s75thbirthday(Harmonic AnalysisandPartialDifferentialEquations:EssaysinHonorofAlbertoCalderón, editedwithM.ChristandC.Kenig,TheUniversityofChicagoPress,1999).Inthe firstvolume,wehaveincludedalistascompleteaspossibleofherscholarlywork. Notablearehercontributionstoharmonicanalysisandoperatortheory,inparticular herlifelongandveryfruitfulcollaborationwithMischaCotlar. When news of Cora’s passing spread like wildfire in December 2010, many people were struck. The mathematical community quickly reacted. The AWM organizedanimpromptumemorialatthe2011JointMathematicalMeeting(JMM), asreportedbyJillPipher,atthetimeAWMpresident: Manypeoplewrotetoexpresstheirsadnessandtosendremembrances.TheAWMbusiness meetingonThursday,January6atthe2011JMMwaslargelydevotedtoaremembranceof Cora. ThisappearedintheMarch-AprilissueoftheAWMNewsletter2whichwasentirely dedicatedtothememoryofCoraSadosky. An obituary by Allyn Jackson for Cora Sadosky appeared in Notices of the AmericanMathematicalSocietyinApril2011.3 In June 2011, Cathy O’Neal wrote in her blog mathbabe4 a beautiful remem- branceforCora: [...] Cora, whom I met when I was 21, was the person that made me realize there is a community of women mathematicians, and that I was also welcome to that world. [...] AndIfelthonoredtohavemetCora,whoseobviouspassionformathematicswasabsolutely awe-inspiring.Shewasthepersonwhofirstexplainedtomethat,aswomenmathematicians, wewillkeepgrowing,keepwriting,andkeepgettingbetteratmathaswegrowolder[...]. WhenIgoogledherthismorning,Ifoundoutshe’ddiedabout6monthsago.Youcanread 2President’s Report, AWM Newsletter, Vol. 41, No. 2, March-April 2011, p. 1. This issue was dedicatedtothememoryofCoraSadoskyanditwaspartiallyreproducedinVolume1. 3NoticesAMS,Vol.58,Number4,April2011,pp.613–614. 4http://mathbabe.org/2011/06/29/cora-sadosky/ PrefaceforVolume2 ix aboutherdifficultandinspiringmathematicalcareerinthisbiography.5Itmademecryand mademethinkabouthowmuchtheworldneedsrolemodelslikeCora. In 2013, the Association for Women in Mathematics established the biennial AWM-SadoskyPrizeinAnalysis,6 tobeawardedeveryotheryearstartingin2014. Thepurposeoftheawardistohighlightexceptionalresearchinanalysisbyawoman earlyinhercareer.SvitlanaMayborodawasthefirstrecipientoftheAWM-Sadosky Research Prize in Analysis awarded in January 2014. Mayboroda contributed a survey paper joint with Ariel Barton to the first of this series of two volumes. As thefirstvolumewentintopress,thesecondrecipientoftheaward,the2016AWM- Sadosky Prize, was announced: Daniela de Silva, from Columbia University. The awardwaspresentedtoherintheJanuary2016JointMathematicalMeeting. In2015,KristinLauter,presidentoftheAWM,startedherreportintheMay-June issueoftheAWMNewsletter,7withacoupleofparagraphsrememberingCora: IrememberveryclearlythedayImetCoraSadoskyatanAWMeventshortlyafterIgotmy PhD,and,knowingverylittleaboutme,shesaidunabashedlythatshedidn’tseeanyreason thatIshouldnotbeaprofessoratHarvardsomeday.Irememberbeingshockedbythisidea, andpleasedthatanyonewouldexpresssuchconfidenceinmypotential,andimpressedat theaudacityofherideasandconfidenceofherconvictions. NowIknowhowshefelt:whenIseetheincrediblytalentedandpassionateyoungfemale researchersinmyfieldofmathematics,Ithinktomyselfthatthereisnoreasononthisearth that some of them should not be professors at Harvard. But we are not there yet ...and therestillremainmanybarrierstotheadvancementandequaltreatmentofwomeninour professionandmuchworktobedone. In these two volumes, friends, colleagues, and/or mentees have contributed research papers, surveys, and/or short remembrances about Cora. The remem- brancesweresometimesweavedintothearticlesubmitted(eitheratthebeginningor theend),andwehaverespectedtheformateachauthorchose.Manyoftheauthors gavetalksinthe13thNewMexicoAnalysisSeminar,inAnAfternooninHonorof Cora Sadosky, and/orintheSpecial SessionsoftheAMS;otherscouldnotattend theseeventsbutdidnotthinktwicewhengiventheopportunitytocontributetothis homage. Themathematical contributions naturally align withCora’s mathematical inter- ests:harmonicanalysisandPDEs,weightednorminequalities,Banachspacesand BMO,operatortheory,complexanalysis,andclassicalFouriertheory. Volume 1 contains articles about Cora and her mathematics and mentorship, remembrances by colleagues and friends, her bibliography according to Math- SciNet,andsurveyandresearcharticlesonharmonicanalysisandpartialdifferential equations, BMO, Banach and metric spaces, and complex and classical Fourier analysis. 5BiographiesofWomeninMathematics:CoraSadoskyhttp://www.agnesscott.edu/lriddle/women/ corasadosky.htm 6MoredetailsintheAWM-SadoskyResearchPrizeinAnalysiswebpage:https://sites.google.com/ site/awmmath/programs/sadosky-prize. 7President’sReport.AWMNewsletter,Vol.45,No.3,May-June,p.1(2015). x PrefaceforVolume2 The year 2014 saw the resolution of the two-weight problem for the Hilbert transformàlaMuckenhouptbyMichaelLacey,ErikSawyer,Chun-YenShen,and Ignacio Uriarte-Tuero, a problem that had been open for 40 years. This problem was solved à la Helson-Szegö by Cora Sadosky and Mischa Cotlar in the early 1980s using complex analysis and operator theory methods. In the last 15 years, a number of techniques have been developed and refined to yield this result, includingstoppingtimearguments,Bellmanfunctions,Lerner’smedianapproach, andbumpedapproach. Volume 2 contains more remembrances and survey and research articles on weightednorminequalities,operatortheory,complexanalysis,dynamicalsystems, and dyadic harmonic analysis. The articles illustrate surprising connections to Tauberian functions, number theory, and wavelet systems. A survey of the two- weightproblemfortheHilberttransformbyMichaelLaceyisfeatured. Beforedescribing indetail the contents of thesecond volume inthisseries,we wouldliketoendwithsomewordsbyNikolaiNikolski8 regardingCoraSadosky’s jointworkwithMischaCotlaronthetwo-weightproblem: MynextimpressiononMischa’smathematicsisdatedabout10yearslaterwhenhisgreat series of papers with Cora Sadosky on Generalized Toeplitz Kernels (GTK) started to appear.Ontheagewhenallpeopleinvolvedin“weightedanalysis”wereexcitedwiththe Muckenhoupt-typeapproach(whichisefficientforrealvariableapplications),theCotlar- Sadosky’s idea to develop Helson-Szegö classical techniques was revolutionary. They immediately obtained important applications of the GTK theory in a variety of domains wherecomplexanalysislanguageismoreappropriatethantherealanalysisone(scattering theory, Hankel and Toeplitz operators, dilation theory..., but also singular integrals for so important problems as the famous two-weighted estimates). This Cotlar-Sadosky seriesappearedalmostsimultaneouslywiththewell-knownKrein’sschoolachievements (Adamyan-Arov-Krein) and the Lax-Phillips approach to scattering theory, but the GTK theoryshowedseveraladvantages(as,forexample,animportant-andgrowingwithtime! -efficiencyinseveralcomplexvariables.) ContentsofVolume2 We now describe in more detail the contents of the second volume. Volume 2 includes remembrances, photos, two survey articles, and research articles by an array of mathematicians representing themes at the heart of Cora’s mathematical interests:weightedinequalities,complexanalysis,andoperatortheory. In the chapter “Remembering Corita”, author and poet Margaret Randall, longtimefriendofCoritaandherparents,ManuelandCora,shareshermemoriesof thefamily,andinchapter“RememberingCora”NeilHindman,HowardUniversity Cora’sformercolleague,sharesafewmemories. 8ThisisaparagraphinaremembranceforMischaCotlarthatcanbefoundatwww.math.unm.edu/ conferences/10thAnalysis/resources/cotlar/nikolski.pdf.
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