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Weak lineal convexity

Christer O. Kiselman (2015)

Banach Center Publications

A bounded open set with boundary of class C¹ which is locally weakly lineally convex is weakly lineally convex, but, as shown by Yuriĭ Zelinskiĭ, this is not true for unbounded domains. The purpose here is to construct explicit examples, Hartogs domains, showing this. Their boundary can have regularity C 1 , 1 or C ∞ . Obstructions to constructing smoothly bounded domains with certain homogeneity properties will be discussed.

Weighted Bergman projections and tangential area integrals

William Cohn (1993)

Studia Mathematica

Let Ω be a bounded strictly pseudoconvex domain in ℂ n . In this paper we find sufficient conditions on a function f defined on Ω in order that the weighted Bergman projection P s f belong to the Hardy-Sobolev space H k p ( ∂ Ω ) . The conditions on f we consider are formulated in terms of tent spaces and complex tangential vector fields. If f is holomorphic then these conditions are necessary and sufficient in order that f belong to the Hardy-Sobolev space H k p ( ∂ Ω ) .

Zeros of bounded holomorphic functions in strictly pseudoconvex domains in ℂ 2

Jim Arlebrink (1993)

Annales de l'institut Fourier

Let D be a bounded strictly pseudoconvex domain in ℂ 2 and let X be a positive divisor of D with finite area. We prove that there exists a bounded holomorphic function f such that X is the zero set of f . This result has previously been obtained by Berndtsson in the case where D is the unit ball in ℂ 2 .

Currently displaying 321 – 340 of 346