简介:探讨加权Bergman空间A^p(φ)上的Carleson型测度和具有非负测度符号的Toeplitz算子,给出Carleson测度或消没Carleson测度的若干等价描述并用Carleson测度的方法刻画了Toeplitz算子是有界的或紧致的充要条件.
简介:主要研究从Dirichlet空间到Bloch空间的某些算子有界性的充要条件以及这些算子与Dirichlet空间上Carleson测度的关系.
简介:<正>WegiveseveralequivalencesofBlochfunctionsandlittleBlochfunetions.UsingtheseresultsweobtainthegeneralizedCarlesonmeasurecharacterizationofBlochfunctionsandthegeneralizedvanishingCarlesonmeasurecharacterizationoflittleBlochfunctions,thatis,f∈Bifandonlyif|Dβf(z)|p(1-|z|2)βp-1dm(z)isageneralizedCarlesonmeasure;f∈B0ifandonlyif|Dβf(z)|p(1-|z|2)βp-1dm(z)isageneralizedvanishingCarlesonmeasure,whereDβf(β>0)isthefractionalderivativeofanalyticfunctionfoforderβ,mdenotesthenormalisedLebesguemeasure.
简介:<正>LetD={z∈:|z|<1}andφbeanormalfunctionon[0,1).Forp∈(0,1)suchafunctionφisusedtodefineaBergmanspaceA~p(φ)onDwithweightφ~p(|·|)/(1-|·|~2).Inthispaper,thedualspaceofA~p(φ)isgiven,fourcharacteristicsofCarlesonmeasureonA~p(φ)areobtained.Moreover,asanapplication,threesequenceinterpolationtheoremsinA~p(φ)arederived.
简介:Let■betheopenunitdiskinthecomplexplane■.Forα>-1,letdA_α(z)=(1+α)1-|z|~2αdA(z)betheweightedLebesguemeasureon■.Forapositivefunctionω∈L~1(■,dA_α),thegeneralizedweightedBergman-OrliczspaceA_ω~ψ(■,dA_α)isthespaceofallanalyticfunctionssuchthat||f||_ω~ψ=∫_■ψ(|f(z)|)ω(z)dA_α(z)<∞,whereψisastrictlyconvexOrliczfunctionthatsatisfiesothertechnicalhypotheses.LetGbeameasurablesubsetof■,wesayGsatisfiesthereverseCarlesonconditionforA_ω~ψ(■,dA_α)ifthereexistsapositiveconstantCsuchthat∫_Gψ(|f(z)|)ω(z)dA_α(z)≥C∫_■ψ(|f(z)|)ω(z)dA_α(z),forallf∈A_ω~ψ(■,dA_α).LetμbeapositiveBorelmeasure,wesayμsatisfiesthedirectCarlesonconditionifthereexistsapositiveconstantMsuchthatforallf∈A_ω~ψ(■,dA_α),∫_■ψ(|f(z)|)dμ(z)≤M∫_■ψ(|f(z)|)ω(z)dA_α(z).Inthispaper,westudythedirectandreverseCarlesonconditiononthegeneralizedweightedBergman-OrliczspaceA_ω~ψ(■,dA_α).WepresentconditionsonthesetGsuchthatthereverseCarlesonconditionholds.Moreover,wegiveasufficientconditionforthefinitepositiveBorelmeasureμtosatisfythedirectcarlesonconditiononthegeneralizedweightedBergman-Orliczspaces.
简介:Carleson型极大算子源于Fourier级数的点态收敛性研究,该算子与振荡奇异积分算子有密切的联系。在Carleson型极大算子的研究中出现了一些不同形式。文章首先将用线性化方法证明两类不同形式的Carleson型极大算子是相等的。其次,文章对于相函数为含有一次项的多项式的情形,将运用Calderon—Zygmund旋转方法证明带粗糙核的Carleson型极大算子LP是有界的,1〈p〈2.