Speaker: Jakub Maksymiuk

Time: 17:00-18:00 pm, February 2, 2023, GMT+8

Venue: Zoom Meeting ID: 872-1512-1661 Password: 256005

Abstract:

The Nemytski operator N_f induced by some function f is a map acting from one function space into another. Its regularity depends on both the smoothness of f and growth conditions imposed on f and its derivatives.
First, I will present some known results about regularity of N_f in Lebesgue spaces and in isotropic Orlicz spaces. These results give the necessary and sufficient conditions for N_f to be well defined, continuous and differentiability up to order k. Next, I want to point out difficulties that arise when one tries to extend these result to anisotropic Orlicz spaces.

Source: School of Mathematical Sciences