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L∞-continuity of Henkin operators solving in certain weakly pseudoconvex domains of ℂ2

Published online by Cambridge University Press:  14 November 2011

Joan Verdera
Joan Verdera
Affiliation:
Facultat de Matemàtiques, Universitat de Barcelona, Gran Via 585, Barcelona 7, Spain
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Extract

Let ψ ∈ C2[0,1] be a positive function on (0, 1]. Under certain assumptions on ψ, the set

is a pseudoconvex domain with C2-boundary, for which it is possible to construct a Henkin-type operator Hψ = Kψ + Bψ solving in Dψ. The operator Bψ, is L∞-continuous because it has a Riesz potential type kernel, while the L∞-continuity of Kψ depends on the flatness of ψ at 0. Our main result states that Kψ is continuous from L∞(∂Dψ) into L∞(Dψ) if and only if

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 99 , Issue 1-2 , 1984 , pp. 25 - 33
Copyright
Copyright © Royal Society of Edinburgh 1984

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References

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