Projective limits of Poletsky--Stessin Hardy spaces

Evgeny A. Poletsky

Projective limits of Poletsky--Stessin Hardy spaces

Complex Variables 2015-03-03 v1

Authors: Evgeny A. Poletsky

Abstract

In this paper we show that that on a strongly pseudoconvex domain $D$ the projective limit of all Poletsky--Stessin Hardy spaces $H^p_u(D)$ , introduced in \cite{PS}, is isomorphic to the space $H^\infty(D)$ of bounded holomorphic functions on $D$ endowed with a special topology. To prove this we show that Carath\'eodory balls lie in approach regions, establish a sharp inequality for the Monge--Amp\'ere mass of the envelope of plurisubharmonic exhaustion functions and use these facts to demonstrate that the intersection of all Poletsky--Stessin Hardy spaces $H^p_u(D)$ is $H^\infty(D)$ .

Keywords

hardy spaces

Cite

@article{arxiv.1503.00575,
  title  = {Projective limits of Poletsky--Stessin Hardy spaces},
  author = {Evgeny A. Poletsky},
  journal= {arXiv preprint arXiv:1503.00575},
  year   = {2015}
}

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