## Harmonic Bergman Functions on Half-Spaces

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- by Wade C. Ramey and HeungSu Yi PDF
- Trans. Amer. Math. Soc.
**348**(1996), 633-660 Request permission

## Abstract:

We study harmonic Bergman functions on the upper half-space of $\mathbf {R}^n$. 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”.## References

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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
- Received by editor(s): October 13, 1994
- © Copyright 1996 American Mathematical Society
- 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