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Gleason's problem for harmonic Bergman and Bloch functions on half-spaces |
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| Authors: | Boo Rim Choe Hyungwoon Koo HeungSu Yi |
| Institution: | (1) Department of Mathematics, Korea University, 136-701 Seoul, Korea;(2) Department of Mathematics, Hankuk University of Foreign Studies, 449-791 Yongin, Kyungki-Do, Korea;(3) Department of Mathematics, Research Institute of Basic Sciences, Kwangwoon University, 139-701 Seoul, Korea |
| Abstract: | On the setting of the half-spaceR n–1×R +, we investigate Gleason's problem for harmonic Bergman and Bloch functions. We prove that Gleason's problem for the harmonicL p -Bergman space is solvable if and only ifp>n. We also prove that Gleason's problem for the harmonic (little) Bloch space is solvable. |
| Keywords: | Primary 31B05 Secondary 31B10 32A35 30D55 |
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