Closed range multiplication operators on weighted Bergman spaces

2005 ◽  
Vol 60 (1) ◽  
pp. 37-48 ◽  
Author(s):  
Kinga Cichoń
Keyword(s):  
Bergman Spaces ◽  
Weighted Bergman Spaces ◽  
Multiplication Operators ◽  
Closed Range

Closed range weighted composition operators on weighted Bergman spaces

2017 ◽  
Vol 24 (4) ◽  
Author(s):  
Elke Wolf
Keyword(s):  
Unit Disk ◽  
Composition Operators ◽  
Bergman Spaces ◽  
Weighted Bergman Spaces ◽  
Open Unit ◽  
Weighted Composition Operators ◽  
Open Unit Disk ◽  
Closed Range ◽  
Weighted Composition

AbstractLet ψ be an analytic map and ϕ an analytic self-map of the open unit disk

scholarly journals Weighted composition operators with closed range

2007 ◽  
Vol 75 (3) ◽  
pp. 331-354 ◽  
Author(s):  
N. Palmberg
Keyword(s):  
Infinite Order ◽  
Composition Operators ◽  
Bergman Spaces ◽  
Sufficient Conditions ◽  
Weighted Bergman Spaces ◽  
Weighted Composition Operators ◽  
Closed Range ◽  
Type Spaces ◽  
Weighted Composition ◽  
Necessary And Sufficient

We study the closed range property of weighted composition operators on weighted Bergman spaces of infinite order (including the Hardy space of infinite order). We give some necessary and sufficient conditions and find a complete characterisation for weighted composition operators associated with conformal mappings. We also give the corresponding results for composition operators on the Bloch-type spaces. Therefore, the results obtained in this paper also improve and generalise the results of Ghatage, Yan, Zheng and Zorboska.

scholarly journals Embedding Theorems and Area Operators on Bergman Spaces with Doubling Measure

2021 ◽  
Vol 15 (3) ◽  
Author(s):  
Changbao Pang ◽  
Antti Perälä ◽  
Maofa Wang
Keyword(s):  
Borel Measure ◽  
Bergman Spaces ◽  
Embedding Theorem ◽  
Weighted Bergman Spaces ◽  
Embedding Theorems ◽  
Positive Borel Measure ◽  
Doubling Property ◽  
Area Operator ◽  
Special Cases ◽  
Upper Half Plane

AbstractWe establish an embedding theorem for the weighted Bergman spaces induced by a positive Borel measure $$d\omega (y)dx$$ d ω ( y ) d x with the doubling property $$\omega (0,2t)\le C\omega (0,t)$$ ω ( 0 , 2 t ) ≤ C ω ( 0 , t ) . The characterization is given in terms of Carleson squares on the upper half-plane. As special cases, our result covers the standard weights and logarithmic weights. As an application, we also establish the boundedness of the area operator.

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