Recent Advances in Harmonic Analysis and Applications: In Honor of Konstantin Oskolkov PDF
Preview Recent Advances in Harmonic Analysis and Applications: In Honor of Konstantin Oskolkov
Springer Proceedings in Mathematics & Statistics Volume 25 Forfurthervolumes: http://www.springer.com/series/10533 Springer Proceedings in Mathematics & Statistics Thisbookseriesfeaturesvolumescomposedofselectcontributionsfromworkshops and conferences in all areas of current research in mathematics and statistics, includingORandoptimization.Inadditiontoanoverallevaluationoftheinterest, scientific quality, and timeliness of each proposal at the hands of the publisher, individual contributions are all refereed to the high quality standards of leading journals in the field. Thus, this series provides the research community with well-edited, authoritative reports on developments in the most exciting areas of mathematicalandstatisticalresearchtoday. Dmitriy Bilyk • Laura De Carli Alexander Petukhov • Alexander M. Stokolos Brett D. Wick Editors Recent Advances in Harmonic Analysis and Applications In Honor of Konstantin Oskolkov 123 Editors DmitriyBilyk LauraDeCarli DepartmentofMathematics DepartmentofMathematics UniversityofSouthCarolina FloridaInternationalUniversity Columbia,SouthCarolina UniversityPark,Miami,Florida USA USA AlexanderPetukhov AlexanderM.Stokolos DepartmentofMathematics DepartmentofMathematics UniversityofGeorgia GeorgiaSouthernUniversity Athens,Georgia Statesboro,Georgia USA USA BrettD.Wick DepartmentofMathematics GeorgiaInstituteofTechnology Atlanta,Georgia USA ISSN2194-1009 ISSN2194-1017(electronic) ISBN978-1-4614-4564-7 ISBN978-1-4614-4565-4(eBook) DOI10.1007/978-1-4614-4565-4 SpringerNewYorkHeidelbergDordrechtLondon LibraryofCongressControlNumber:2012948608 MathematicsSubjectClassification(2010):42-XX,35-XX,11Zxx,5T60,8Wxx ©SpringerScience+BusinessMedia,LLC2013 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof thematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation, broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology nowknownorhereafterdeveloped.Exemptedfromthislegalreservationarebriefexcerptsinconnection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. 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Printedonacid-freepaper SpringerispartofSpringerScience+BusinessMedia(www.springer.com) KonstantinOskolkov DrawnbyNikolayOskolkov Preface This volume is dedicated to Konstantin Oskolkov’s 65th birthday and is a cel- ebration of his contributions to mathematical analysis. It grew out of the AMS SectionalMeetingheldatGeorgiaSouthernUniversity,March11–13,2011.Many ofthechaptersappearingin thisvolumeareclose toKostya’sbroadmathematical interests. The editors wish to thank all those who made this volume possible. Special thanksgotoalltheauthorswhohavecontributedchapterstothisvolume.Wealso wanttoacknowledgethetimeandthehardworkofthereferees. Columbia,SC,USA DmitriyBilyk Miami,FL,USA LauraDeCarli Athens,GA,USA AlexanderPetukhov Statesboro,GA,USA AlexanderM.Stokolos Atlanta,GA,USA BrettD.Wick vii Contents PartI KonstantinOskolkov OntheScientificWorkofKonstantinIlyichOskolkov ...................... 3 DmitriyBilyk,LauraDeCarli,AlexanderPetukhov,Alexander M.Stokolos,andBrettD.Wick K.I.Oskolkov .................................................................... 23 MagomedA.Chakhkiev MyFirstMeetingswithKonstantinOskolkov................................ 27 ViktorI.Kolyada MeetingswithKostyaOskolkov................................................ 31 VeniaminG.Krotov KonstantinIlyichOskolkov,FriendandColleague .......................... 35 MichaelT.Lacey TheActivityofK.I.OskolkovinNonlinearApproximation ofFunctions....................................................................... 39 VitalyMaiorov HowYoungWeWere ............................................................ 43 VladimirTemlyakov PartII ContributedPapers ASurveyofMultidimensionalGeneralizationsofCantor’s UniquenessTheoremforTrigonometricSeries............................... 49 J.MarshallAsh TheL DiscrepancyofTwo-DimensionalLattices............................ 63 2 DmitriyBilyk,VladimirN.Temlyakov,andRuiYu ix x Contents OnFourierMultipliersOverTubeDomains.................................. 79 LauraDeCarli Multiparameter ProjectionTheorems with Applications to Sums-ProductsandFinite Point Configurationsin the EuclideanSetting................................................................. 93 BurkErdog˘an,DerrickHart,andAlexIosevich RieszPotentials,BesselPotentials,andFractionalDerivatives onBesov-LipschitzSpacesfortheGaussianMeasure ....................... 105 A.EduardoGatto,EbnerPineda,andWilfredoO.Urbina Maximal Operators Associated to Sets of Directions ofHausdorffandMinkowskiDimensionZero................................ 131 PaulHagelstein DistanceGraphsinVectorSpacesOverFiniteFields........................ 139 Derrick Hart, Alex Iosevich, Doowon Koh, Steven Senger, andIgnacioUriarte-Tuero RemarksonExtremalsinMinimalSupportInequalities.................... 161 StevenM.Hudson OnFubiniTypePropertyinLorentzSpaces.................................. 171 ViktorI.Kolyada SomeApplicationsofEquimeasurableRearrangements.................... 181 AnatoliiA.KorenovskiiandAlexanderM.Stokolos MaximalFunctionsMeasuringSmoothness .................................. 197 VeniaminG.Krotov EstimatesfortheExceptionalLebesgueSetsofFunctionsfrom SobolevClasses................................................................... 225 VeniaminG.KrotovandMikhailA.Prokhorovich OntheA InequalityforCaldero´n–ZygmundOperators................... 235 2 MichaelT.Lacey QuestforNegativeDependencyGraphs....................................... 243 LinyuanLu,AustinMohr,andLa´szlo´ Sze´kely A Quantitative Open Mapping Theorem for Quasi- PseudonormedGroups .......................................................... 259 IrinaMitrea,MariusMitrea,andEliaZiade´ TheBuckleyDyadicSquareFunction ......................................... 287 FedorNazarovandMichaelWilson L∞-BoundsfortheL2-ProjectionontoLinearSplineSpaces................ 303 PeterOswald
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