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Closed range multiplication operators on weighted Bergman spaces

✍ Scribed by Kinga Cichoń

Publisher
Elsevier Science
Year
2005
Tongue
English
Weight
207 KB
Volume
60
Category
Article
ISSN
0362-546X

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✦ Synopsis

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) = (d(z, *S)), : R + → R + , 0, defined on a strip S or weights w(z) = (Re z) , > -1 p , defined on a right half plane.

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