## Analysis and PDE

•  Alexey Karapetyants
•  On Bergman type spaces of functions of nonstandard growth and some related questions.
•  11/14/2018
•  4:10 PM - 5:00 PM
•  C517 Wells Hall

Abstracts: We study various Banach spaces of holomorphic functions on the unit disc and half plane. As a main question we investigate the boundedness of the corresponding holomorphic projection. We exploit the idea of V.P.Zaharyuta, V.I.Yudovich (1962) where the boundedness of the Bergman projection in Lebesgue spaces was proved using Calderon-Zygmund operators. We treat the cases of variable exponent Lebesgue space, Orlicz space, Grand Lebesgue space and variable exponent generalized Morrey space. The major idea is to show that the approach can be applied to a wide range of function spaces. This opens a door in a sense for introducing and studying new function spaces of Bergman type in complex analysis. We also study the rate of growth of functions near the boundary in spaces under consideration and their approximation by mollifying dilations.

## Contact

Department of Mathematics
Michigan State University