## Evgeny Poletsky (11/06/15)

Math Colloquium

### Speaker: Evgeny Poletsky, Syracuse University

Title: Hardy spaces on hyperconvex domains: recent advances

Location: Naustið, Endurmenntun (here)

Time: Thursday, June 11, at 15:00-16:00.

### Abstract:

In 2008 M. Stessin and the speaker introduced on a general hyperconvex domain \(D\) the spaces of holomorphic functions \(H^p_u(D)\) as analogs of the classical Hardy spaces on the unit disk. This spaces are parameterized by plurisubharmonic exhaustion functions \(u\) of \(D\). When \(D\) is strictly pseudoconvex they all are the subsets of classical Hardy spaces \(H^p(D)\) and coincide with \(H^p(D)\) when \(u\) is a pluricomplex Green function.

In my talk we will provide all necessary definitions and discuss recent advances: complete description of these spaces on the unit disk and their projective limits on strongly pseudoconvex domains.