Projective Limits of Poletsky–Stessin Hardy Spaces

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In this paper we show that on a strongly pseudoconvex domain D the projective limit of all Poletsky–Stessin Hardy spaces Hup(D), introduced by Poletsky and Stessin in 2008, is isomorphic to the space H(D) of bounded holomorphic functions on D endowed with a special topology. To prove this we show that Carathéodory balls lie in approach regions, establish a sharp inequality for the Monge–Ampére mass of the envelope of plurisubharmonic exhaustion functions and use these facts to demonstrate that the intersection of all Poletsky–Stessin Hardy spaces Hup(D) is H(D).

Original languageEnglish (US)
Pages (from-to)1001-1016
Number of pages16
JournalComplex Analysis and Operator Theory
Issue number5
StatePublished - Jun 1 2016


  • Hardy spaces
  • Pluricomplex Green function
  • Pluripotential theory
  • Strongly pseudoconvex domains

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics
  • Computational Theory and Mathematics


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