Hilbert-Schmidt Hankel operators with anti-holomorphic symbols on a class of unbounded complete Reinhardt domains

被引：0
|
作者：
He, Le [1 ]
Tang, Yanyan [2 ]
机构：
[1] Wuhan Inst Technol, Sch Math & Phys, 206 Guanggu 1st Rd, Wuhan 430070, Hubei, Peoples R China
[2] Henan Univ, Sch Math & Stat, 85 Minglun St, Kaifeng 475001, Henan, Peoples R China
来源：
CZECHOSLOVAK MATHEMATICAL JOURNAL | 2024年 / 74卷 / 04期
基金：
中国国家自然科学基金;
关键词：
unbounded complete Reinhardt domain; Hankel operator; Hilbert-Schmidt operator; BERGMAN SPACES; RIGIDITY; MAPPINGS; KERNEL;
D O I：
10.21136/CMJ.2024.0067-24
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We consider a class of unbounded nonhyperbolic complete Reinhardt domains D-n,m,k(mu,p,s):={(z, w(1), . . . , w(m))is an element of C(n)xC(k1)x. . .xC(km):& Vert;w1 & Vert;(2p1)/ e(-mu 1 & Vert;z & Vert;s)+. . .+& Vert;w(m)& Vert;(2pm)/ e(-mu m & Vert;z & Vert;s)<1} wheres,p1, . . . , pm,mu 1, . . . , mu mare positive real numbers andn,k1, . . . , kmare positiveintegers. We show that if a Hankel operator with anti-holomorphic symbolis Hilbert-Schmidt on the Bergman space A(2)(D-n,m,k(mu,p,s)), then it must be zero. This gives an exampleof high dimensional unbounded complete Reinhardt domain that does not admit nonzeroHilbert-Schmidt Hankel operators with anti-holomorphic symbols
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页码：1097 / 1112
页数：16
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