Projective Limits of Poletsky–Stessin Hardy Spaces

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

In this paper we show that on a strongly pseudoconvex domain D the projective limit of all Poletsky–Stessin Hardy spaces (Formula presented.), introduced by Poletsky and Stessin in 2008, is isomorphic to the space (Formula presented.) 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 (Formula presented.) is (Formula presented.).

Original languageEnglish (US)
Pages (from-to)1-16
Number of pages16
JournalComplex Analysis and Operator Theory
DOIs
StateAccepted/In press - Dec 26 2015

Fingerprint

Projective Limit
Hardy Space
Topology
Plurisubharmonic Function
Pseudoconvex Domain
Sharp Inequality
Envelope
Analytic function
Ball
Isomorphic
Intersection
Demonstrate

Keywords

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

ASJC Scopus subject areas

  • Applied Mathematics
  • Computational Mathematics
  • Computational Theory and Mathematics

Cite this

Projective Limits of Poletsky–Stessin Hardy Spaces. / Poletsky, Evgeny Alexander.

In: Complex Analysis and Operator Theory, 26.12.2015, p. 1-16.

Research output: Contribution to journalArticle

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