News

Seminario: “On the boundedness of Bergman projection in various new Banach spaces and some related questions“

Venerdì 16 Febbraio 2018, ore 12:15 - Aula 1BC45 - Alexey Karapetyants

ARGOMENTI: Seminars

Venerdì 16 Febbraio 2018 alle ore 12:15 in Aula 1BC45, Alexey Karapetyants (Southern Federal University e Don State Technical Universityi (Rostov sul Don - Russia) terrà una conferenza dal titolo “On the boundedness of Bergman projection in various new Banach spaces and some related questions”.

Abstract
We give an approach to the proof of the boundedness of Bergman projection in various new Banach spaces of functions on the unit disc/half space in the complex plain. The approach is based on the use of Calderon-Zygmund operators. We exploit this approach and treat the cases of variable exponent Lebesgue space, Orlicz space, variable exponent generalized Morrey space, and Grand/Small Lebesgue spaces. 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.