scholarly journals Toeplitz Operators on Higher Cauchy–Riemann Spaces Over the Unit Ball

2018 ◽  
Vol 90 (6) ◽  
Author(s):  
Lijia Ding ◽  
Kai Wang
Keyword(s):  
Unit Ball ◽  
Toeplitz Operators ◽  
Cauchy Riemann

Complex Symmetric Toeplitz Operators on the Unit Polydisk and the Unit Ball

2019 ◽  
Vol 40 (1) ◽  
pp. 35-44 ◽  
Author(s):  
Cao Jiang ◽  
Xingtang Dong ◽  
Zehua Zhou
Keyword(s):  
Unit Ball ◽  
Toeplitz Operators ◽  
Unit Polydisk ◽  
Complex Symmetric

scholarly journals Properties of Commutativity of Dual Toeplitz Operators on the Orthogonal Complement of Pluriharmonic Dirichlet Space over the Ball

2016 ◽  
Vol 2016 ◽  
pp. 1-9
Author(s):  
Yinyin Hu ◽  
Yufeng Lu ◽  
Tao Yu
Keyword(s):  
Sobolev Space ◽  
Unit Ball ◽  
Toeplitz Operators ◽  
Dirichlet Space ◽  
Orthogonal Complement ◽  
Pluriharmonic Functions

We completely characterize the pluriharmonic symbols for (semi)commuting dual Toeplitz operators on the orthogonal complement of the pluriharmonic Dirichlet space in Sobolev space of the unit ball. We show that, forfandgpluriharmonic functions,SfSg=SgSfon(Dh)⊥if and only iffandgsatisfy one of the following conditions:(1)bothfandgare holomorphic;(2)bothf¯andg¯are holomorphic;(3)there are constantsαandβ, both not being zero, such thatαf+βgis constant.

scholarly journals Compact Toeplitz operators on weighted harmonic Bergman spaces

1998 ◽  
Vol 64 (1) ◽  
pp. 136-148 ◽  
Author(s):  
Karel Stroethoff
Keyword(s):  
Unit Ball ◽  
Harmonic Functions ◽  
Toeplitz Operators ◽  
Bergman Spaces ◽  
Harmonic Bergman Spaces

AbstractWe consider the Bergman spaces consisting of harmonic functions on the unit ball in Rn that are squareintegrable with respect to radial weights. We will describe compactness for certain classes of Toeplitz operators on these harmonic Bergman spaces.

scholarly journals Algebras of Toeplitz Operators on the n-Dimensional Unit Ball

2018 ◽  
Vol 13 (2) ◽  
pp. 493-524 ◽  
Author(s):  
Wolfram Bauer ◽  
Raffael Hagger ◽  
Nikolai Vasilevski
Keyword(s):  
Unit Ball ◽  
Toeplitz Operators ◽  
Algebras Of Toeplitz Operators ◽  
Dimensional Unit

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.

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