scholarly journals Toeplitz Operators and Division Theorems in Anisotropic Spaces of Holomorphic Functions in the Polydisc

2003 ◽  
Vol 48 (4) ◽  
pp. 347-363 ◽  
Author(s):  
A.V. Harutyunyan
Keyword(s):  
Toeplitz Operators ◽  
Holomorphic Functions ◽  
Spaces Of Holomorphic Functions ◽  
Anisotropic Spaces

scholarly journals Bloch spaces of holomorphic functions in the polydisk

2007 ◽  
Vol 5 (3) ◽  
pp. 213-230 ◽  
Author(s):  
Anahit Harutyunyan
Keyword(s):  
Holomorphic Functions ◽  
Bloch Spaces ◽  
Spaces Of Holomorphic Functions ◽  
Diagonal Mapping ◽  
Anisotropic Spaces

This work is an introduction to anisotropic spaces of holomorphic functions, which haveω-weight and are generalizations of Bloch spaces to a polydisc. We prove that these classes form an algebra and are invariant with respect to monomial multiplication. Some theorems on projection and diagonal mapping are proved. We establish a description of(Ap(ω))*(or(Hp(ω))*via the Bloch classes for all0<p≤1.

scholarly journals Toeplitz operators on weighted spaces of holomorphic functions

2008 ◽  
Vol 103 (1) ◽  
pp. 40 ◽  
Author(s):  
Anahit Harutyunyan ◽  
Wolfgang Lusky
Keyword(s):  
Toeplitz Operator ◽  
Unit Disk ◽  
Essential Spectrum ◽  
Complex Plane ◽  
Toeplitz Operators ◽  
Holomorphic Functions ◽  
Weighted Spaces ◽  
Norm Estimates ◽  
Spaces Of Holomorphic Functions

We define a notion of Toeplitz operator on certain spaces of holomorphic functions on the unit disk and on the complex plane which are endowed with a weighted sup-norm. We establish boundedness and compactness conditions, give norm estimates and characterize the essential spectrum of these operators for many symbols.

scholarly journals Traces of certain classes of holomorphic functions on finite unions of Carleson sequences

1999 ◽  
Vol 41 (1) ◽  
pp. 103-114 ◽  
Author(s):  
ANDREAS HARTMANN
Keyword(s):  
Holomorphic Functions ◽  
Spaces Of Holomorphic Functions ◽  
Hardy Classes ◽  
Type Spaces ◽  
Trace Spaces

We give a method allowing the generalization of the description of trace spaces of certain classes of holomorphic functions on Carleson sequences to finite unions of Carleson sequences. We apply the result to different classes of spaces of holomorphic functions such as Hardy classes and Bergman type spaces.

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