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

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
Copyright
Copyright © Royal Society of Edinburgh 1984

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References

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