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

DOI:
https://doi.org/10.1090/S0002-9947-96-01383-9

MathSciNet review:
1303125

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Abstract | References | Similar Articles | Additional Information

Abstract: We study harmonic Bergman functions on the upper half-space of . Among our main results are: The Bergman projection is bounded for the range ; certain nonorthogonal projections are bounded for the range ; the dual space of the Bergman -space is the harmonic Bloch space modulo constants; harmonic conjugation is bounded on the Bergman spaces for the range ; 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:
https://doi.org/10.1090/S0002-9947-96-01383-9

Keywords:
Bergman kernel,
projection operators,
dual spaces,
harmonic Bloch space

Received by editor(s):
October 13, 1994

Article copyright:
© Copyright 1996
American Mathematical Society