The 𝐻² corona problem and \overline∂_{𝑏} in weakly pseudoconvex domains

Andersson, Mats

doi:10.1090/S0002-9947-1994-1145727-3

The $H^ 2$ corona problem and $\overline \partial _ b$ in weakly pseudoconvex domains
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by Mats Andersson

Trans. Amer. Math. Soc. 342 (1994), 241-255

DOI: https://doi.org/10.1090/S0002-9947-1994-1145727-3

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Abstract:

We derive a Bochner-Kodaira-Nakano-Morrey-Kohn-Hörmander type equality in holomorphic vector bundles and obtain ${L^2}$-estimates for ${\bar \partial _b}$ in a pseudoconvex domain that admits a plurisubharmonic ${C^2}$ defining function. We combine these with the trick in Wolff’s proof of the corona theorem and obtain a ${H^2}$-corona theorem in such a domain.

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Smooth pseudoconvex domains in

for which the corona theorem and

estimates for

fail

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