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- W2073318098 abstract "A weighted Bergman space B is a Banach space of the form L p ( μ )∩Hol( Ω ), where μ is a Borel measure carried by the bounded region Ω in the complex plane. We consider closed subspaces M of B that are invariant for multiplication by the independent variable z . We say M has the division property, if dim M /( z − λ ) M =1 for each λ ∈ Ω . In terms of the local boundary behavior of the functions in M we give several conditions which imply the division property. For example, this happens if M is generated by functions that extend analytically near a fixed boundary point and if ∂ Ω is nice near this point. “Analytic” may be replaced by “locally Nevanlinna.” For the standard weights (1−| z |) α dA on the unit disc we show that M has the division property if it contains one function that is locally Nevanlinna near a boundary point. Furthermore, in the unweighted case ( α =0) the invariant subspace generated by two functions that are L r respectively L s (1/ r +1/ s =1/ p ) near some boundary point, has the division property." @default.
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- W2073318098 date "1997-03-01" @default.
- W2073318098 modified "2023-09-30" @default.
- W2073318098 title "Some Sufficient Conditions for the Division Property of Invariant Subspaces in Weighted Bergman Spaces" @default.
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- W2073318098 doi "https://doi.org/10.1006/jfan.1996.2998" @default.
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