指数型加权Bergman空间上Hankel算子的有界性与紧性  

The Boundness and Compactness of Hankel Operators on Exponential Bergman Spaces

作　　者：林殷淇 夏锦[1] LIN Yinqi;XIA Jin(College of Mathematics and Information Science,Guangzhou University,Guangzhou 510006,China)

机构地区：[1]广州大学数学与信息科学学院,广州510006

出　　处：《四川轻化工大学学报（自然科学版）》2024年第4期92-100,共9页Journal of Sichuan University of Science & Engineering(Natural Science Edition)

基　　金：国家自然科学基金项目(11971125)。

摘　　要：令φ为一类指数型权,对于单位圆盘D上由指数型权诱导的加权Bergman空间A_(φ)^(p)=L_(φ)^(p)∩H(D),其中H(D)为单位圆盘D上全体全纯函数所成的空间,其上的Hankel算子记作H_(f)(g)=(Id-P)(fg)。本文介绍了指数型权的基本性质以及证明有界性与紧性所需要的相关定理与引理,并对空间上的再生核函数以及∂ˉ方程的解做出了某些积分估计和范数估计。然后利用前面积分估计与范数估计的结果得出:当1≤p≤q<∞时,分别得到了Hankel算子H_(f)从A_(φ)^(p)到Lebesgue空间L_(φ)^(q)的有界性与紧性的等价刻画;当1≤q<p<∞时,Hankel算子H_(f)从A_(φ)^(p)到Lebesgue空间L_(φ)^(q)的有界性与紧性是彼此等价的。Letφbe a exponential weight,Apφ=Lpφ∩H(D)denotes the exponential Bergman spaces on D,where H(D)denotes the spaces of all analytic functions in the D unit disk.The Hankel operators on Apφdenoted by Hf(g)=(Id-P)(fg).The basic properties of exponential weights and the relevant theorems and lemmas required for proving are introduced,some integral estimates and norm estimates of reproducing kernel functions and∂ˉestimates are given.Then,by using the integral estimation results obtained above,the boundedness and compactness on the Bergman space of exponential weight of the unit disk is obtained:when 1≤p≤q<∞,Hankel operators Hf is bound and compact from Apφonto Lqφ,expecially when 1≤q<p<∞,Hankel operators Hf is boundness and compactness from Apφonto Lqφis necessary and sufficiency.

关 键 词：指数型加权Bergman空间 HANKEL算子 有界性 紧性 

分 类 号：O177[理学—数学]