Toeplitz operators on weighted Besov spaces of holomorphic functions on the polydisk

2015 ◽  
Vol 50 (4) ◽  
pp. 176-186
Author(s):  
A. Harutyunyan ◽  
W. Lusky
Keyword(s):  
Besov Spaces ◽  
Toeplitz Operators ◽  
Holomorphic Functions ◽  
Spaces Of Holomorphic Functions ◽  
Weighted Besov Spaces

scholarly journals Weighted holomorphic Besov spaces on the polydisk

2011 ◽  
Vol 9 (1) ◽  
pp. 1-16 ◽  
Author(s):  
Anahit V. Harutyunyan ◽  
Wolfgang Lusky
Keyword(s):  
Fractional Derivative ◽  
Besov Space ◽  
Besov Spaces ◽  
Regular Variation ◽  
Holomorphic Functions ◽  
Spaces Of Holomorphic Functions ◽  
Weighted Besov Spaces ◽  
Unit Polydisk ◽  
Projection Theorems ◽  
Dimensional Lebesgue Measure

This work is an introduction of weighted Besov spaces of holomorphic functions on the polydisk. LetUnbe the unit polydisk inCnandSbe the space of functions of regular variation. Let1≤p<∞,ω=(ω1,…,ωn),ωj∈S(1≤j≤n)andf∈H(Un).The functionfis said to be an element of the holomorphic Besov spaceBp(ω)if‖f‖Bp(ω)p=∫Un|Df(z)|p∏j=1nωj(1-|zj|)/(1-|zj|2)2-pdm2n(z)<+∞, wheredm2n(z)is the2n-dimensional Lebesgue measure onUnandDstands for a special fractional derivative offdefined in the paper. For example, ifn=1thenDfis the derivative of the functionzf(z).We describe the holomorphic Besov space in terms ofLp(ω)space. Moreover projection theorems and theorems of the existence of a right inverse are proved.

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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