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.
Join Zoom Meeting:
Meeting ID: 872 1512 1661