Association for Women in Mathematics Series María Cristina Pereyra Stefania Marcantognini Alexander M. Stokolos Wilfredo Urbina Editors Harmonic Analysis, Partial Diff erential Equations, Complex Analysis, Banach Spaces, and Operator Theory (Volume 1) Celebrating Cora Sadosky's life Association for Women in Mathematics Series Volume 4 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, Complex Analysis, Banach Spaces, and Operator Theory (Volume 1) Celebrating Cora Sadosky’s life 123 Editors MaríaCristinaPereyra StefaniaMarcantognini DepartmentofMathematicsandStatistics DepartmentofMathematics UniversityofNewMexico VenezuelanInstituteforScientificResearch Albuquerque,NewMexico,USA Caracas,Venezuela AlexanderM.Stokolos WilfredoUrbina DepartmentofMathematicalSciences DepartmentofMathematicsandActuarial GeorgiaSouthernUniversity Science Statesboro,Georgia,USA RooseveltUniversity Chicago,Illinois,USA ISSN2364-5733 ISSN2364-5741 (electronic) AssociationforWomeninMathematicsSeries ISBN978-3-319-30959-0 ISBN978-3-319-30961-3 (eBook) DOI10.1007/978-3-319-30961-3 LibraryofCongressControlNumber:2016946423 ©SpringerInternationalPublishingSwitzerland2016 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof thematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation, broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology nowknownorhereafterdeveloped. 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Printedonacid-freepaper ThisSpringerimprintispublishedbySpringerNature TheregisteredcompanyisSpringerInternationalPublishingAGSwitzerland PhotographbyMargaretRandall,February2,2004 Preface for Volume 1 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 morethana100analysts—fledgling,junior,andsenior,fromallovertheUSAand the world such as: Canada, India, Mexico, Sweden, the UK, South Korea, Brazil, Israel, Hungary, Finland, Australia, and Spain—to remember her outspokenness, her uncompromising ways, her sharp sense of humor, her erudition, and above all herprofoundloveformathematics. 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 and then back to Buenos Aires, from Caracas to the USA and then back to Buenos Aires, and from Washington, D.C., to California. HeremindedusofCoraalwaysstandingupforhumanrights,Coraaspresidentof theAssociationforWomeninMathematics(AWM),andCoraalwaysencouraging andfightingforwhatshethoughtwasright. 1The 13th New Mexico Analysis Seminar and An Afternoon in Honor of Cora Sadosky were sponsored by National Science Foundation (NSF) grant DMS-140042, the Simons Foundation, andtheEfroymsonFoundation,andtheeventsweredoneincooperationwiththeAssociationfor WomeninMathematics(AWM).Seetheconference’swebsites: www.math.unm.edu/conferences/13thAnalysis people.math.umass.edu/~nahmod/CoraSadosky.html AnAfternooninHonorofCoraSadoskywasorganizedbyAndreaNahmod,CristinaPereyra, andWilfredoUrbina.The13thNewMexicoAnalysisSeminarorganizerswereMattBlair,Cristina PereyraAnnaSkripka,MaximZinchenkofromUniversityofNewMexico,andNickMichalowsky fromNewMexicoStateUniversity. vii viii PrefaceforVolume1 Cora was born in Buenos Aires, Argentina, on May 23, 1940, and died on December3,2010,inLongBeach,CA.CoragotherPhDin1965attheUniversity of Chicago under the supervision of both Alberto Calderón and Antoni Zygmund, 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,whobrightenedtheirlastyears.Duringherlife,Corawrotemorethan50 researchpapers,andagraduatetextbookonInterpolationofOperatorsandSingular 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, CRC Press, 1989) and one celebrating Alberto Calderón 75th birthday (Harmonic AnalysisandPartialDifferentialEquations:EssaysinHonorofAlbertoCalderón, edited with M. Christ and C. Kenig, The University of Chicago Press, 1999). We haveincludedalistascompleteaspossibleofherscholarlywork.Notableareher contributions to harmonic analysis and operator theory, in particular her lifelong veryfruitfulcollaborationwithMischaCotlar. 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,atthetimetheAWMpresident: 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’sReport,AWMNewsletter,Vol.41,No.2,March–April 2011, p.1.Thisissuewas dedicatedtothememoryofCoraSadosky. 3NoticesAMS,Vol.58,Number4,April2011,pp.613–614. 4http://mathbabe.org/2011/06/29/cora-sadosky/. PrefaceforVolume1 ix aboutherdifficultandinspiringmathematicalcareerinthisbiography.5Itmademecryand mademethinkabouthowmuchtheworldneedsrolemodelslikeCora. In 2013, the Association for Women in Mathematics established the biennial AWM-SadoskyPrizeinAnalysis,6 tobeawardedeveryotheryearstartingin2014. Thepurposeoftheawardistohighlightexceptionalresearchinanalysisbyawoman earlyinhercareer.SvitlanaMayborodawasthefirstrecipientoftheAWM-Sadosky ResearchPrizeinAnalysisawardedinJanuary2014.Mayborodaiscontributinga survey paper joint with Ariel Barton to this volume. We include the press release issuedbytheAWMonMay15,2013,andthecitationandMayboroda’s response that appeared in the March–April 2014 issue of the AWM Newsletter.7 As this volumegoesintopress,thesecondrecipientoftheaward,the2016AWM-Sadosky Prize,wasannounced:DanieladaSilva,fromColumbiaUniversity. In2015,KristinLauter,presidentoftheAWM,startedherreportintheMay–June issueoftheAWMNewsletter,8withacoupleofparagraphsrememberingCora: 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(eitheratthebeginingor theend),andwehaverespectedtheformateachauthorchose.Manyoftheauthors gavetalksinthe13thNewMexicoAnalysisSeminar,inAnAfternooninHonorof Cora Sadosky, and/or in the special sessions of the AMS; others could not attend theseeventsbutdidnotthinktwicewhengiventheopportunitytocontributetothis homage. The mathematical contributions naturally align withCora’s mathematical inter- ests:harmonicanalysisandPDEs,weightednorminequalities,Banachspacesand BMO,operatortheory,complexanalysis,andclassicalFouriertheory. Volume1containsarticlesaboutCora,hermathematicsandmentorship,remem- brancesbycolleaguesandfriends,herbibliographyaccordingtoMathSciNet,and 5BiographiesofWomeninMathematics:CoraSadoskyhttp://www.agnesscott.edu/lriddle/women/ corasadosky.htm. 6MoredetailsintheAWM-SadoskyResearchPrizeinAnalysiswebpage:https://sites.google.com/ site/awmmath/programs/sadosky-prize. 7AWMNewsletter,Volume44,Number2,March–April2014. 8President’sReport.AWMNewsletter,Vol.45,No.3,May–June,p.1.