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arXiv · 1110.1533

Duality of holomorphic functions spaces und smoothing properties of the Bergman projection

Anne-Katrin Herbig·Jeffery D. McNeal·Emil J. Straube
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Abstract

Let $Ω\subset\mathbb{C}^n$ be a bounded domain with smooth boundary, whose Bergman projection $B$ maps the Sobolev space $H^{k_{1}}(Ω)$ (continuously) into $H^{k_{2}}(Ω)$. We establish two smoothing results: (i) the full Sobolev norm $\|Bf\|_{k_{2}}$ is controlled by $L^2$ derivatives of $f$ taken along a single, distinguished direction (of order $\leq k_{1}$), and (ii) the projection of a conjugate holomorphic function in $L^{2}(Ω)$ is automatically in $H^{k_{2}}(Ω)$. There are obvious corollaries for when $B$ is globally regular.

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Anne-Katrin Herbig, Jeffery D. McNeal, Emil J. Straube. 2011-10-07. Duality of holomorphic functions spaces und smoothing properties of the Bergman projection. https://arxiv.org/abs/1110.1533

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