摘要
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.
出版日期
2017年03月13日（中国期刊网平台首次上网日期，不代表论文的发表时间）
