Numerical range of composition operators on weighted Hardy spaces

2007 ◽  
Vol 2 ◽  
pp. 1341-1346 ◽  
Author(s):  
B. Yousefi ◽  
S. Haghkhah
Keyword(s):  
Hardy Spaces ◽  
Numerical Range ◽  
Composition Operators ◽  
Weighted Hardy Spaces

scholarly journals Spatial Numerical Range of Operators on Weighted Hardy Spaces

2011 ◽  
Vol 2011 ◽  
pp. 1-8 ◽  
Author(s):  
Abdolaziz Abdollahi ◽  
Mohammad Taghi Heydari
Keyword(s):  
Hardy Spaces ◽  
Finite Rank ◽  
Numerical Range ◽  
Compact Operators ◽  
Weighted Hardy Spaces ◽  
Finite Rank Operators

We consider the spatial numerical range of operators on weighted Hardy spaces and give conditions for closedness of numerical range of compact operators. We also prove that the spatial numerical range of finite rank operators on weighted Hardy spaces is star shaped; though, in general, it does not need to be convex.

Generalized composition operators on weighted Hardy spaces

2012 ◽  
Vol 218 (17) ◽  
pp. 8347-8352 ◽  
Author(s):  
Stevo Stević ◽  
Ajay K. Sharma
Keyword(s):  
Hardy Spaces ◽  
Composition Operators ◽  
Weighted Hardy Spaces

On Dirichlet Spaces With a Class of Superharmonic Weights

2018 ◽  
Vol 70 (4) ◽  
pp. 721-741 ◽  
Author(s):  
Guanlong Bao ◽  
Nihat Gokhan Göğüş ◽  
Stamatis Pouliasis
Keyword(s):  
Hardy Spaces ◽  
Carleson Measure ◽  
Reproducing Kernel ◽  
Boundary Behavior ◽  
Composition Operators ◽  
Open Unit ◽  
Dirichlet Spaces ◽  
Weighted Hardy Spaces ◽  
Borel Measures ◽  
Infinite Sum

AbstractIn this paper, we investigate Dirichlet spaces with superharmonic weights induced by positive Borel measures μ on the open unit disk. We establish the Alexander-Taylor-Ullman inequality for spaces and we characterize the cases where equality occurs. We define a class of weighted Hardy spaces via the balayage of the measure μ. We show that is equal to if and only if μ is a Carleson measure for . As an application, we obtain the reproducing kernel of when μ is an infinite sum of point-mass measures. We consider the boundary behavior and innerouter factorization of functions in . We also characterize the boundedness and compactness of composition operators on .

Norms of composition operators on weighted Hardy spaces

2013 ◽  
Vol 196 (1) ◽  
pp. 273-283 ◽  
Author(s):  
Eva A. Gallardo-Gutiérrez ◽  
Jonathan R. Partington
Keyword(s):  
Hardy Spaces ◽  
Composition Operators ◽  
Weighted Hardy Spaces
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