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L 2-estimates with Levi-singular weight, and existence for\(\overline \partial \)

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Abstract

We give a symplectic proof of the link between pseudoconvexity of domains ofC n and of their boundaries (cf. [7, Th. 2.6.12]). Our approach also allows us to treat boundaries of codimension >1. We then extend the estimates by Hörmander in [7, Ch. 4, 5] and [6] toL 2-norms which haveC 1 but notC 2 weights and under a less restrictive assumption of weakq-pseudoconvexity. (A special trick is needed as a substitute for the method of thelowest positive eigenvalue of [6].)

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  1. v. Miglioranza 20, Vicenza, Italy

    Giuseppe Zampieri

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  1. Giuseppe Zampieri
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Zampieri, G. L 2-estimates with Levi-singular weight, and existence for\(\overline \partial \) . J. Anal. Math. 74, 99–111 (1998). https://doi.org/10.1007/BF02819447

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  • DOI: https://doi.org/10.1007/BF02819447

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