Abstract
We study harmonic Bergman functions on the upper half-space of R n \mathbf {R}^n . Among our main results are: The Bergman projection is bounded for the range 1 > p > ∞ 1> p > \infty ; certain nonorthogonal projections are bounded for the range 1 ≤ p > ∞ 1\leq p > \infty ; the dual space of the Bergman L 1 L^1 -space is the harmonic Bloch space modulo constants; harmonic conjugation is bounded on the Bergman spaces for the range 1 ≤ p > ∞ 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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