Abstract:
In the work we introduce the Orlicz spaces on the base of nonlinear nonlocal functionals. We study the main properties of such spaces. We prove that these spaces are Banach, separable and the set of compactly supported infinitely differentiable functions is dense in these spaces. We describe the structure of dual spaces and obtain the representations for the linear functionals.
Keywords:Orlicz space, convolution type functional, functional of variable growth.
