Computational Methods and Function Theory 2 (2002), No. 2, 579--596
Copyright Heldermann Verlag 2002
Eric D. Schippers
schip@umich.edu, University of Michigan, East Hall, 525 E. University Ave., Ann Arbor, MI, 48109-1109, U.S.A.
Inequalities for derivatives of the Bergman and $L$-kernel are derived for elliptically schlicht domains, using the Dirichlet Principle. By introducing a generalization of elliptically schlicht domains involving metrics of constant positive curvature, it is seen that the inequalities smoothly interpolate the bounded, unbounded and elliptically schlicht cases.
Keywords: Elliptically schlicht, univalent, Bergman kernel, Green's function, inequalities, conformal metrics, elliptic capacity, Dirichlet Principle.
MSC 2000: 30C40, 30C45, 30C55, 30C75.
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