## Evgeny Poletsky (11/06/15)

Benedikt Magnússon, júní 9, 2015

Málstofa í stærðfræði

### Fyrirlesari: Evgeny Poletsky, Syracuse University Titill: Hardy spaces on hyperconvex domains: recent advances

Staðsetning: Naustið, Endurmenntun (hér)
Tími: Fimmtudagur 11. júní, klukkan 15:00-16:00.

### Ágrip:

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.