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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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
Email: ramey@math.msu.edu

HeungSu Yi
Affiliation: Global Analysis Research Center, Department of Mathematics, Seoul National University, Seoul, Korea #151-742
Email: hsyi@math.snu.ac.kr

DOI: http://dx.doi.org/10.1090/S0002-9947-96-01383-9
PII: S 0002-9947(96)01383-9
Keywords: Bergman kernel, projection operators, dual spaces, harmonic Bloch space
Received by editor(s): October 13, 1994
Article copyright: © Copyright 1996 American Mathematical Society