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A Class of Operators on Weighted Bergman Spaces

✍ Scribed by Miyeon Kwon; Zhijian Wu

Publisher
SP Birkhäuser Verlag Basel
Year
2008
Tongue
English
Weight
147 KB
Volume
62
Category
Article
ISSN
0378-620X

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Providence) concerning bounded composition operators on weighted Bergman spaces of the unit disk. The main result is the following: if G i = e -h i for i = 1 2 are weight functions in a certain range for which h 1 r /h 2 r → ∞ as r → 1 then there is a self-map of the unit disk such that the induced

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✍ Kinga Cichoń 📂 Article 📅 2005 🏛 Elsevier Science 🌐 English ⚖ 207 KB

Let be a bounded analytic function on a simply connected domain ⊆ C. For a large family of weights we characterize when a pointwise multiplication operator M , M (f )(z)= (z)f (z), defined on a weighted Bergman space A p w ( ) on has closed range. In particular, the result holds for weights w(z) = (