应用泛函分析学报
應用汎函分析學報
응용범함분석학보
ACTA ANALYSIS FUNCTIONALIS APPLICATA
2011年
3期
246-259
,共14页
Bergman空间%Bergman距离%极大函数%面积函数%Bergman积分算子
Bergman空間%Bergman距離%極大函數%麵積函數%Bergman積分算子
Bergman공간%Bergman거리%겁대함수%면적함수%Bergman적분산자
Bergman space%Bergman metric%maximal function%area function%Bergman integral operator
介绍复球上Bergman空间实变理论的某些新进展,包括Bergman空间关于Carleson矩形的实变原子分解,极大函数和面积函数刻画以及运用帐篷空间的实变刻画.特别是,用齐次空间上向量值Calderón-Zygmund奇异积分算子理论研究Bergman积分算子的Lp有界性并给出了Bergman空间面积积分刻画的新证明.
介紹複毬上Bergman空間實變理論的某些新進展,包括Bergman空間關于Carleson矩形的實變原子分解,極大函數和麵積函數刻畫以及運用帳篷空間的實變刻畫.特彆是,用齊次空間上嚮量值Calderón-Zygmund奇異積分算子理論研究Bergman積分算子的Lp有界性併給齣瞭Bergman空間麵積積分刻畫的新證明.
개소복구상Bergman공간실변이론적모사신진전,포괄Bergman공간관우Carleson구형적실변원자분해,겁대함수화면적함수각화이급운용장봉공간적실변각화.특별시,용제차공간상향량치Calderón-Zygmund기이적분산자이론연구Bergman적분산자적Lp유계성병급출료Bergman공간면적적분각화적신증명.
In this paper,we give a survey of results obtained recently by the present authors on real-variable characterizations of Bergman spaces,which are closely related to maximal and area integral functions in terms of the Bergman metric.In particular,we give a new proof of those results concerning area integral characterizations through using the method of vector-valued CalderónZygmund operators to handle Bergman singular integral operators on the complex ball.The proofs involve some sharp estimates of the Bergman kernel function and Bergman metric.
