Peak functions on weakly pseudoconvex domains. (English) Zbl 0828.32003

The main result of this paper gives a new sufficient condition for a boundary point of a domain to be a peak point for the uniform algebra of holomorphic functions that are continuous on the closure of the domain. The condition is that the boundary is pseudoconvex there, and the Catlin’s multitype agrees with D’Angelo’s \(q\)-types. We also provide other equivalent formulations.


32T99 Pseudoconvex domains
32F45 Invariant metrics and pseudodistances in several complex variables
32A38 Algebras of holomorphic functions of several complex variables
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