Smooth Pseudoconvex Domains in ℂ2 For Which the Corona Theorem and Lp Estimates for ∂̄ Fail
Let Ω be a bounded domain in Cn and let H 8(Ω) denote the algebra of bounded holomorphic functions in Ω. The problem of whether Ω is dense in the spectrum of H 8(Ω) (corona problem) has attracted some attention. The answer is known to be affirmative for many open sets in C ; see Ref. 4 for a discussion. The answer is not known in ℂ n n ≥ 2 even for the ball or the polydisk.
KeywordsHolomorphic Function Smooth Boundary Pseudoconvex Domain Subharmonic Function Reinhardt Domain
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