The korenblum maximum principle for some function spaces
We study the Korenblum Maximum Principle on the weighted Fock space Fpα(C) and the weighted Bergman space Apα(D) under the gaussian weight e−pα2|z|2. We obtain explicit expressions for the upper bounds of Korenblum constants for the weighted Fock space Fpα(C), p ≥ 1 and α > 0. Then, we obtain u...
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| Format: | Final Year Project |
| Language: | English |
| Published: |
2019
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| Subjects: | |
| Online Access: | http://hdl.handle.net/10356/77142 |
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| Institution: | Nanyang Technological University |
| Language: | English |
| Summary: | We study the Korenblum Maximum Principle on the weighted Fock space Fpα(C) and the weighted Bergman space Apα(D) under the gaussian weight e−pα2|z|2.
We obtain explicit expressions for the upper bounds of Korenblum constants for
the weighted Fock space Fpα(C), p ≥ 1 and α > 0. Then, we obtain upper bounds
of such constants for the weighted Bergman space Apα(D), p ≥ 1 and α ≥ 0.
We also show a failure of the Korenblum Maximum Principle for weighted
Bergman space Apα(D), where 0 < p < 1, α > 0, thus bringing closure of the
problem under weighted Bergman space Apα(D) where α > 0. |
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