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

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- by Mats Andersson PDF
- Trans. Amer. Math. Soc.
**342**(1994), 241-255 Request permission

## 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.## References

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*Smooth pseudoconvex domains in*${\mathbb {C}^2}$

*for which the corona theorem and*${L^p}$

*estimates for*$\bar \partial$

*fail*, preprint 1991.

## Additional Information

- © Copyright 1994 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**342**(1994), 241-255 - MSC: Primary 32F15; Secondary 32F05, 32F20, 46J15
- DOI: https://doi.org/10.1090/S0002-9947-1994-1145727-3
- MathSciNet review: 1145727