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Sharp Hölder estimates for $\overline {\partial }$ on ellipsoids
and their complements via order of contact

Author: Julian F. Fleron
Journal: Proc. Amer. Math. Soc. 124 (1996), 3193-3202
MSC (1991): Primary 32F10, \, 32F20
MathSciNet review: 1363459
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Abstract: We generalize the results of Range and Diederich et al., finding Hölder estimates for the solution of the Cauchy-Riemann equations for higher order forms on ellipsoids. We prove a dual result near the concave boundaries of complemented complex ellipsoids. In all cases the Hölder exponents are characterized in terms of the order of contact of the boundary of the domain with complex linear spaces of the appropriate dimension. Optimality is demonstrated in the convex settings, and for $(0,1)$ forms in the concave setting. Partial results are given for complemented real ellipsoids and a method for demonstrating optimality of Hortmann's result on complemented strictly pseudoconvex domains is given for $(0,1)$ forms.

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Additional Information

Julian F. Fleron
Affiliation: Department of Mathematics, Westfield State College, Westfield, Massachusetts 01086
Email: J_Fleron@FOMA.WSC.Mass.Edu

Received by editor(s): April 10, 1995
Additional Notes: This work is part of the authors Ph.D. dissertation at SUNY University at Albany, and was completed while the author was a U.S. Department of Education Fellow. \endgraf The author would like to express his gratitude to his advisor Prof. R.M. Range for his continued guidance and support.
Communicated by: Eric Bedford
Article copyright: © Copyright 1996 American Mathematical Society