第40卷第4期2023年7月新疆大学学报（自然科学版）（中英文）JournalofXinjiangUniversity(NaturalScienceEditioninChineseandEnglish)Vol.40,No.4Jul.,2023Two-WeightNormEstimatesforHausdorffOperators∗YANGShuai,LIBaode†(SchoolofMathematicsandSystemSciences,XinjiangUniversity,UrumqiXinjiang830017,China)Abstract:Two-weightinequalitiesforHausdorffoperatorshavebeenestablishedinweightedLebesguespacesundercertainassumptionsofkernelfunction.WestudytheHausdorffoperatorsofspecialkindonthereallineR+andalsoestablishcorre-spondingtwo-weightinequalitiesunderweakerassumptionsofkernelfunction.Thenwegivesomespecificexamplesthatsatisfytheseconditionsofkernelfunction.Keywords:Hausdorffoperators;weightedLebesguespaces;weightfunctionDOI：10.13568/j.cnki.651094.651316.2022.11.12.0001CLCnumber：O177.6DocumentCode：AArticleID：2096-7675(2023)04-0398-07引文格式：杨帅,李宝德.Hausdorff算子的双权范数估计[J].新疆大学学报(自然科学版)(中英文),2023,40(4):398-404.英文引文格式：YANGShuai,LIBaode.Two-weightnormestimatesforHausdorffoperators[J].JournalofXinjiangUniver-sity(NaturalScienceEditioninChineseandEnglish),2023,40(4):398-404.Hausdorff算子的双权范数估计杨帅，李宝德(新疆大学数学与系统科学学院，新疆乌鲁木齐830017)摘要：Hausdorff算子的核函数在满足一定条件时,其在加权Lebesgue空间上的双权不等式已经被建立．研究了定义在R+上的Hausdorff算子,当Hausdorff算子的核函数在更弱的条件下仍能建立相应的双权不等式,并给出了满足这种条件的具体核函数的例子．关键词：Hausdorff算子；加权Lebesgue空间；权函数0IntroductionandMainResultsFixalocallyintegrablefunctionφontheinterval(0,∞).Theone-dimensionalHausdorffoperatorHφisdefinedbyHφf(x)=�∞0φ(xy)yf(y)dy.Forthesakeofsimplicity,weinitiallyassumethatfunctionsfareintheclassofSchwartzfunctions.TheHausdorffoperatorisdeeplyrootedinthestudyofone-dimensionalFourieranalysisandhasbecomeanessentialpartofmodernharmonicanalysis.Inparticular,itiscloselyrelatedtothesummabilityoftheclassicalFourierseries[1].Additionally,manyclassicaloperatorsinanalysisarespecialcasesoftheHausdorffoperatorifo...
