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Harmonic Bergman Functions on Half-Spaces

Authors: Wade C. Ramey and HeungSu Yi
Journal: Trans. Amer. Math. Soc. 348 (1996), 633-660
MSC (1991): Primary 31B05; Secondary 31B10, 30D55, 30D45
MathSciNet review: 1303125
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Abstract: We study harmonic Bergman functions on the upper half-space of $\bold{R}^n$. Among our main results are: The Bergman projection is bounded for the range $1< p < \infty$; certain nonorthogonal projections are bounded for the range $1\leq p < \infty$; the dual space of the Bergman $L^1$-space is the harmonic Bloch space modulo constants; harmonic conjugation is bounded on the Bergman spaces for the range $1\leq p < \infty$; the Bergman norm is equivalent to a ``normal derivative norm'' as well as to a ``tangential derivative norm''.

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Additional Information

Wade C. Ramey
Affiliation: Department of Mathematics, Michigan State University, East Lansing, Michigan 48824-1027

HeungSu Yi
Affiliation: Global Analysis Research Center, Department of Mathematics, Seoul National University, Seoul, Korea #151-742

Keywords: Bergman kernel, projection operators, dual spaces, harmonic Bloch space
Received by editor(s): October 13, 1994
Article copyright: © Copyright 1996 American Mathematical Society

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