Nonlocal convolution type functionals and related Orlicz spaces

TL;DR

This paper introduces a new class of Orlicz-type functional spaces based on nonlocal convolution integrals, establishing their fundamental properties, duality, and providing illustrative examples.

Contribution

It defines and analyzes nonlocal convolution-based Orlicz spaces, proving they are Banach and separable under certain conditions, and characterizes their dual spaces.

Findings

Spaces are Banach and separable

Dual spaces are characterized

Examples illustrate the theory

Abstract

In the paper we introduce Orlicz type functional spaces defined in terms of nonlocal convolution type integral functionals and study the main properties of these spaces. We show in particular that, under natural convexity and growth conditions on the integrand, the corresponding spaces are Banach and separable. We also characterize the dual spaces and provide a number of examples.