PhD students and postdoctoral researchers to be supported by a research grant in SabanciUniversity, Istanbul, Turkey. Candidate PhD students should have a good background in mathematical analysis, specifically in complex and functional analysis, and should be motivated to write a PhD thesis and research papers. Postdoctoral researchers are expected to have a PhD in relevant fields. The postdoctoral researcher should be eager to contribute to the research with the other project team.

Project title: Carleson Measures For Sub-Hardy Spaces

Duration: 24 months

Start time: Estimated start time is September 2014

Monthly net stipend of the scholars

PhD student 1800 TL ‘=’ 790 USD

Postoctoral researcher 2250 TL ‘=’ 1015 USD

**In campus housing is available for the scholars free of charge.**

The time for joining the project may be flexible.

Project summary

The subject of the project is analytic function theory in the complex plane. Its main purpose is to adopt and study the Carleson inequalities, which are mostly well-known for the classical Hardy space theory, besides with the reverse Carleson inequalities, in the setup of Poletsky-Stessin spaces. Carleson measures are the mainstream subject of nowadays. The famous theorem of Carleson describes when the Hardy space Hp embeds into the Lp space of a given positive finite measure on the unit disk. This theorem has been extended to several other spaces, like Bergman, Fock, and model spaces. Recently reverse Carleson inequalities have been studied in the classical Hardy space and model spaces. Direct and reverse Carleson measures for Poletsky-Stessin spaces defined on planar regular domains will be investigated in the proposed project. As an application boundedness or compactness of the composition and Toeplitz operators will be studied. I can send the interested ones any of the references below (except Duren).

References

ALAN, M. A., GOGUS, N. G., Poletsky-Stessin-Hardy spaces in the plane, Complex Analysis and Operator Theory, DOI:10.1007/s11785-013-0334-2, arXiv:1209.2609.

BLANDİGNERES, A., FRICAIN, E., GAUNARD, F., HARTMANN, A., ROSS, W. T., Direct and reverse Carleson measures for H(b) spaces, arXiv:1308.1574.

DUREN, P. L., Theory of H^{p} spaces, Pure and Applied Mathematics, Vol. 38 Academic Press, New York-London, (1970).

POLETSKY, E. A., STESSIN, M. I., Hardy and Bergman spaces on hyperconvex domains and their composition operators, Indiana Univ. Math. J. 57 (2008), no. 5, 2153–2201.

Contact information

Gökhan Göğüş

nggogus@sabanciuniv.edu

(216) 483 9615

SabanciUniversity, Istanbul