Smooth Pseudoconvex Domains in ℂ2 For Which the Corona Theorem and Lp Estimates for ∂̄ Fail

  • John Erik Fornaess
  • Nessim Sibony
Part of the The University Series in Mathematics book series (USMA)


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.


Holomorphic Function Smooth Boundary Pseudoconvex Domain Subharmonic Function Reinhardt Domain 
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Copyright information

© Springer Science+Business Media New York 1993

Authors and Affiliations

  • John Erik Fornaess
    • 1
  • Nessim Sibony
    • 2
  1. 1.Department of MathematicsUniversity of MichiganAnn ArborUSA
  2. 2.C.N.R.S. UA 57Université de Paris-SudOrsay CedexFrance

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