Harmonic Bergman Functions on Half-Spaces

Ramey, Wade; Yi, HeungSu

doi:10.1090/S0002-9947-96-01383-9

Harmonic Bergman Functions on Half-Spaces
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by Wade C. Ramey and HeungSu Yi

Trans. Amer. Math. Soc. 348 (1996), 633-660

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

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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”.

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