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Sharp hölder estimates for\(\overline \partial \) on ellipsoids

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Abstract

We solve the\(\overline \partial \)-equation on real and on complex ellipsoids in ℂN. It is proved that the solution satisfies sharp Hölder estimates. That is, the Hölder exponent equals the reciprocal of the maximal order of contact of the boundary of the ellipsoid with complex-analytic curves.

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Authors and Affiliations

  1. Bergische Universität-GHS, Gaussstr.20, D-5600, Wuppertal 1, Federal Republic of Germany

    Klas Diederich

  2. Department of Mathematics, Fine Hall-Washington Road, 08544, Princeton, New Jersey, USA

    John Erik Fornæss & Jan Wiegerinck

Authors
  1. Klas Diederich
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  2. John Erik Fornæss
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  3. Jan Wiegerinck
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Additional information

Supported by NSF grant DMS 8401273.

Supported by the Netherlands' organization for the advancement of pure research ZWO.

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Diederich, K., Fornæss, J.E. & Wiegerinck, J. Sharp hölder estimates for\(\overline \partial \) on ellipsoids. Manuscripta Math 56, 399–417 (1986). https://doi.org/10.1007/BF01168502

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  • DOI: https://doi.org/10.1007/BF01168502

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