四川轻化工大学学报（自然科学版）2024，Vol.37Issue(4)：92-100,9.DOI:10.11863/j.suse.2024.04.11
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
摘要
Abstract
Let φ be 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 Apφ denoted 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 ∂ˉ estimates 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 Apφ onto Lqφ,expecially when 1≤q<p<∞,Hankel operators Hf is boundness and compactness from Apφ onto Lqφ is necessary and sufficiency.关键词
指数型加权Bergman空间/Hankel算子/有界性/紧性Key words
exponential Bergman spaces/Hankel operators/boundness/compactness分类
数理科学引用本文复制引用
林殷淇,夏锦..指数型加权Bergman空间上Hankel算子的有界性与紧性[J].四川轻化工大学学报（自然科学版）,2024,37(4):92-100,9.基金项目
国家自然科学基金项目(11971125) （11971125）
