𝒩(p, q, s)-type spaces in the unit ball of ℂn(II): Carleson measure and its application

2020 ◽  
Vol 32 (1) ◽  
pp. 79-94 ◽  
Author(s):  
Bingyang Hu ◽  
Songxiao Li
Keyword(s):  
Unit Ball ◽  
Carleson Measure ◽  
Bergman Spaces ◽  
Weighted Bergman Spaces ◽  
Weighted Hardy Spaces ◽  
Hadamard Products ◽  
New Class ◽  
Random Power Series ◽  
Type Spaces ◽  
Formula Type

AbstractThe purpose of this paper is to study a new class of function spaces, called {\mathcal{N}(p,q,s)}-type spaces, in the unit ball {{\mathbb{B}}} of {{\mathbb{C}}^{n}}. The Carleson measure on such spaces is investigated. Some embedding theorems among {\mathcal{N}(p,q,s)}-type spaces, weighted Bergman spaces and weighted Hardy spaces are established. As for applications, the Hadamard products and random power series on {\mathcal{N}(p,q,s)}-type spaces are also studied.

Embedding Theorems for Dirichlet Type Spaces

2019 ◽  
Vol 63 (1) ◽  
pp. 106-117 ◽  
Author(s):  
Songxiao Li ◽  
Junming Liu ◽  
Cheng Yuan
Keyword(s):  
Carleson Measure ◽  
Bergman Spaces ◽  
Embedding Theorem ◽  
Weighted Bergman Spaces ◽  
Borel Measures ◽  
Dirichlet Type ◽  
Volterra Operators ◽  
Type Spaces ◽  
Dirichlet Type Spaces ◽  
Analytic Function Spaces

AbstractWe use the Carleson measure-embedding theorem for weighted Bergman spaces to characterize the positive Borel measures $\unicode[STIX]{x1D707}$ on the unit disc such that certain analytic function spaces of Dirichlet type are embedded (compactly embedded) in certain tent spaces associated with a measure $\unicode[STIX]{x1D707}$. We apply these results to study Volterra operators and multipliers acting on the mentioned spaces of Dirichlet type.

Weighted composition operators on weighted Bergman spaces induced by doubling weights

2020 ◽  
Vol 126 (3) ◽  
pp. 519-539
Author(s):  
Juntao Du ◽  
Songxiao Li ◽  
Yecheng Shi
Keyword(s):  
Composition Operators ◽  
Bergman Spaces ◽  
Essential Norm ◽  
Weighted Bergman Spaces ◽  
Weighted Composition Operators ◽  
Schatten Class ◽  
Doubling Weight ◽  
Doubling Weights ◽  
Type Spaces ◽  
Weighted Composition

In this paper, we investigate the boundedness, compactness, essential norm and the Schatten class of weighted composition operators $uC_\varphi $ on Bergman type spaces $A_\omega ^p $ induced by a doubling weight ω. Let $X=\{u\in H(\mathbb{D} ): uC_\varphi \colon A_\omega ^p\to A_\omega ^p\ \text {is bounded}\}$. For some regular weights ω, we obtain that $X=H^\infty $ if and only if ϕ is a finite Blaschke product.

scholarly journals Multiplicative Isometries and Isometric Zero-Divisors

2010 ◽  
Vol 62 (5) ◽  
pp. 961-974 ◽  
Author(s):  
Alexandru Aleman ◽  
Peter Duren ◽  
María J. Martín ◽  
Dragan Vukotić
Keyword(s):  
Banach Spaces ◽  
Bloch Space ◽  
Bergman Spaces ◽  
Weighted Bergman Spaces ◽  
Zero Divisors ◽  
Pointwise Multipliers ◽  
Type Spaces ◽  
Dirichlet Type Spaces ◽  
Coefficient Multipliers ◽  
Spaces Of Analytic Functions

AbstractFor some Banach spaces of analytic functions in the unit disk (weighted Bergman spaces, Bloch space, Dirichlet-type spaces), the isometric pointwise multipliers are found to be unimodular constants. As a consequence, it is shown that none of those spaces have isometric zero-divisors. Isometric coefficient multipliers are also investigated.

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