Essential Norms and Schatten(-Herz) Classes of Integration Operators from Bergman Spaces to Hardy Spaces

被引：9
作者：
Chen, Jiale [1 ]
Pau, Jordi [2 ]
Wang, Maofa [1 ]
机构：
[1] Wuhan Univ, Sch Math & Stat, Wuhan 430072, Peoples R China
[2] Univ Barcelona, Dept Matemat & Informat, Barcelona 08007, Catalonia, Spain
来源：
RESULTS IN MATHEMATICS | 2021年 / 76卷 / 02期
关键词：
Integration operator; Hardy space; Bergman space; compactness; essential norm; Schatten-Herz class;
D O I：
10.1007/s00025-021-01403-8
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we completely characterize the compactness of the Volterra type integration operators J(b) acting from weighted Bergman spaces A(alpha)(p) a to Hardy spaces H-q for all 0 < p, q < infinity. Furthermore, we give some estimates for the essential norms of J(b) : A(alpha)(p) -> H-q in the case 0 < p <= q < infinity. We finally describe the membership in the Schatten(Herz) class of the Volterra type integration operators.
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页数：33
相关论文
共 23 条
[1]  
Ahern P., 1988, Rev. Mat. Iberoam., V4, P123, DOI DOI 10.4171/RMI/66
[2]  
[Anonymous], 1938, Duke Math. J
[3]   Embedding derivatives of M-harmonic functions into Lp spaces [J].
Arsenovic, M .
ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 1999, 29 (01) :61-76
[4]   COMMUTATORS OF SINGULAR INTEGRAL OPERATORS [J].
CALDERON, AP .
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 1965, 53 (05) :1092-&
[5]   AN INTERPOLATION PROBLEM FOR BOUNDED ANALYTIC FUNCTIONS [J].
CARLESON, L .
AMERICAN JOURNAL OF MATHEMATICS, 1958, 80 (04) :921-930
[6]   INTERPOLATIONS BY BOUNDED ANALYTIC FUNCTIONS AND CORONA PROBLEM [J].
CARLESON, L .
ANNALS OF MATHEMATICS, 1962, 76 (03) :547-&
[7]   Asymptotic behavior of eigenvalues of Toeplitz operators on the weighted analytic spaces [J].
El-Fallah, O. ;
Mahzouli, H. ;
Marrhich, I. ;
Naqos, H. .
JOURNAL OF FUNCTIONAL ANALYSIS, 2016, 270 (12) :4614-4630
[8]  
HORMANDER L, 1967, MATH SCAND, V20, P65
[9]   SCHATTEN(-HERZ) CLASS EXTENDED CESARO OPERATORS ON BERGMAN SPACES IN THE UNIT BALL OF Cn [J].
Hu, Zhangjian ;
Tang, Xiaomin .
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2010, 138 (08) :2803-2814
[10]  
Kohr M, 2005, STUD U BABES-BOL MAT, V50, P129
123