Toeplitz operators on weighted Bergman spaces on finitely connected domains

被引：0

作者：

Gogus, Nihat Gokhan ^{[1
]}

Sonmez, Sinem Yelda ^{[1
]}

机构：

[1] Sabanci Univ, Fac Engn & Nat Sci, TR-34956 Istanbul, Turkiye

来源：

ANNALS OF FUNCTIONAL ANALYSIS | 2023年 / 14卷 / 03期

关键词：

Bergman spaces; Carleson measures; Kernel estimate; Toeplitz operator; Composition operator;

D O I：

10.1007/s43034-023-00268-y

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the weighted Bergman spaces on finitely connected planar domains. They are isomorphic to the product of weighted Bergman spaces on the unit disk. Using this, we characterize the Carleson embeddings and prove kernel estimates. We characterize bounded, compact and Schatten class composition and Toeplitz operators on these spaces. Our results generalize several recent ones in the unit disk or simply connected case.

引用

页数：40

共 21 条

[1] HILBERT-SPACES OF ANALYTIC-FUNCTIONS BETWEEN THE HARDY AND THE DIRICHLET SPACE [J].

ALEMAN, A .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1992, 115 (01) :97-104

[2]

Armitage D.H., 2001, SPRINGER MG MATH, DOI [10.1007/978-1-4471-0233-5, DOI 10.1007/978-1-4471-0233-5]

[3] HARMONIC-FUNCTIONS FROM A COMPLEX-ANALYSIS VIEWPOINT [J].

AXLER, S .

AMERICAN MATHEMATICAL MONTHLY, 1986, 93 (04) :246-258

[4]

Bao G., 2017, IEEE INT SYMP CIRC S, V70, P1

[5]

Berenstein CA., 1991, COMPLEX VARIABLES IN, P1188

[6]

Berndtsson B, 2001, OHIO ST U M, V9, P43

[7]

CHEVREAU B, 1981, J OPERAT THEOR, V6, P375

[8] Reproducing Kernels of Some Weighted Bergman Spaces [J].

Deng, Guan-Tie ;

Huang, Yun ;

Qian, Tao .

JOURNAL OF GEOMETRIC ANALYSIS, 2021, 31 (10) :9527-9550

[9] 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

[10] Toeplitz operators on harmonically weighted Bergman spaces and applications to composition operators on Dirichlet spaces [J].

El-Fallah, Omar ;

Mahzouli, Houssame ;

Marrhich, Ibrahim ;

Naqos, Hatim .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2018, 466 (01) :471-489

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