scholarly journals Weighted estimates for the Berezin transform and Bergman projection on the unit ball

2016 ◽  
Vol 286 (3-4) ◽  
pp. 1465-1478 ◽  
Author(s):  
Rob Rahm ◽  
Edgar Tchoundja ◽  
Brett D. Wick
Keyword(s):  
Unit Ball ◽  
Berezin Transform ◽  
Bergman Projection ◽  
Weighted Estimates

scholarly journals Sharp Weighted Bounds for Multilinear Fractional Type Operators Associated with Bergman Projection

2018 ◽  
Vol 2018 ◽  
pp. 1-9
Author(s):  
Juan Zhang ◽  
Senhua Lan ◽  
Qingying Xue
Keyword(s):  
Maximal Function ◽  
Bergman Projection ◽  
Weighted Estimates ◽  
Fractional Maximal Function ◽  
Multiple Weights ◽  
Fractional Type

We first introduce the multiple weights which are suitable for the study of Bergman type operators. Then, we give the sharp weighted estimates for multilinear fractional Bergman operators and fractional maximal function.

BOUNDED TOEPLITZ AND HANKEL PRODUCTS ON THE WEIGHTED BERGMAN SPACES OF THE UNIT BALL

2015 ◽  
Vol 99 (2) ◽  
pp. 237-249
Author(s):  
MAŁGORZATA MICHALSKA ◽  
PAWEŁ SOBOLEWSKI
Keyword(s):  
Unit Ball ◽  
Toeplitz Operators ◽  
Hankel Operator ◽  
Bergman Spaces ◽  
Sufficient Conditions ◽  
Berezin Transform ◽  
Weighted Bergman Space ◽  
Weighted Bergman Spaces ◽  
Necessary Condition ◽  
Sufficient Condition

Let $A_{{\it\alpha}}^{p}$ be the weighted Bergman space of the unit ball in ${\mathcal{C}}^{n}$, $n\geq 2$. Recently, Miao studied products of two Toeplitz operators defined on $A_{{\it\alpha}}^{p}$. He proved a necessary condition and a sufficient condition for boundedness of such products in terms of the Berezin transform. We modify the Berezin transform and improve his sufficient condition for products of Toeplitz operators. We also investigate products of two Hankel operators defined on $A_{{\it\alpha}}^{p}$, and products of the Hankel operator and the Toeplitz operator. In particular, in both cases, we prove sufficient conditions for boundedness of the products.

The Berezin Transform and Radial Operators on the Bergman Space of the Unit Ball

2011 ◽  
Vol 7 (1) ◽  
pp. 313-329 ◽  
Author(s):  
Ze-Hua Zhou ◽  
Wei-Li Chen ◽  
Xing-Tang Dong
Keyword(s):  
Unit Ball ◽  
Bergman Space ◽  
Berezin Transform ◽  
Radial Operators

scholarly journals A Sharp Constant for the Bergman Projection

2015 ◽  
Vol 58 (1) ◽  
pp. 128-133 ◽  
Author(s):  
Marijan Marković
Keyword(s):  
Unit Ball ◽  
Besov Space ◽  
Projection Operator ◽  
Bergman Projection ◽  
Hyperbolic Metric ◽  
Sharp Constant ◽  
The Hyperbolic Metric

AbstractFor the Bergman projection operator P we prove thatHere λ stands for the hyperbolic metric in the unit ball B of Cn, and B1 denotes the Besov space with an adequate semi-norm. We also consider a generalization of this result. This generalizes some recent results due to Perälä.

scholarly journals Berezin transform on the quantum unit ball

2003 ◽  
Vol 44 (9) ◽  
pp. 4344
Author(s):  
Dmitry Shklyarov ◽  
Genkai Zhang
Keyword(s):  
Unit Ball ◽  
Berezin Transform

scholarly journals Multiplication Operator with BMO Symbols and Berezin Transform

2015 ◽  
Vol 2015 ◽  
pp. 1-4
Author(s):  
Xue Feng ◽  
Kan Zhang ◽  
Jianguo Dong ◽  
Xianmin Liu ◽  
Chi Guan
Keyword(s):  
Unit Ball ◽  
Bergman Space ◽  
Sufficient Conditions ◽  
Multiplication Operator ◽  
Berezin Transform ◽  
Weighted Bergman Space ◽  
Necessary And Sufficient Conditions ◽  
Special Symbol ◽  
Necessary And Sufficient

We discuss multiplication operator with a special symbol on the weighted Bergman space of the unit ball. We give the necessary and sufficient conditions for the compactness of multiplication operator on the weighted Bergman space of the unit ball.

scholarly journals Toeplitz operators on the Bergman space of the unit ball

2000 ◽  
Vol 62 (2) ◽  
pp. 273-285 ◽  
Author(s):  
Roberto Raimondo
Keyword(s):  
Unit Ball ◽  
Bergman Space ◽  
Toeplitz Operators ◽  
Berezin Transform ◽  
Finite Products ◽  
Finite Sum

We prove that if an operator A is a finite sum of finite products of Toeplitz operators on the Bergman space of the unit ball Bn, then A is compact if and only if its Berezin transform vanishes at the boundary. For n = 1 the result was obtained by Axler and Zheng in 1997.

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