scholarly journals A Note on Reducing Subspaces of Toeplitz Operator on the Weighted Analytic Function Spaces of the Bidisk Hw2D2

2017 ◽  
Vol 2017 ◽  
pp. 1-4
Author(s):  
Hongzhao Lin
Keyword(s):  
Analytic Function ◽  
Toeplitz Operator ◽  
Toeplitz Operators ◽  
Function Spaces ◽  
Type I ◽  
Reducing Subspaces ◽  
Analytic Function Spaces

We discussed the reducing subspaces of Toeplitz operators Tz1Nz2M  N≠M on the weighted analytic function spaces of bidisk Hw2(D2). The result shows that if the weight w is of type-I, the structure of reducing subspaces of Tz1Nz2M  N≠M on Hw2D2 is very simple.

scholarly journals Norm of a Volterra Integral Operator on Some Analytic Function Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Hao Li ◽  
Songxiao Li
Keyword(s):  
Analytic Function ◽  
Integral Operator ◽  
Unit Disc ◽  
Function Spaces ◽  
Volterra Integral Operator ◽  
Analytic Function Spaces

Let f be an analytic function in the unit disc 𝔻. The Volterra integral operator If is defined as follows: If(h)(z)=∫0zf(w)h'(w)dw,h∈H(𝔻),z∈𝔻. In this paper, we compute the norm of If on some analytic function spaces.

scholarly journals On composition operators inQKtype spaces

2007 ◽  
Vol 5 (2) ◽  
pp. 103-122 ◽  
Author(s):  
Marko Kotilainen
Keyword(s):  
Banach Space ◽  
Analytic Function ◽  
Composition Operator ◽  
Composition Operators ◽  
Bloch Space ◽  
Function Spaces ◽  
Analytic Mapping ◽  
Analytic Function Spaces

Letp≥1,q>-2and letK:[0,∞)→[0,∞)be nondecreasing. With a different choice ofp,q,K, the Banach spaceQK(p,q)coincides with many well-known analytic function spaces. Boundedness and compactness of the composition operatorCφfromα-Bloch spaceBαintoQK(p,q)are characterized by a condition depending only on analytic mappingφ:𝔻→𝔻. The same properties are also studied in the caseCφ:QK(p,q)→Bα.

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