Stepanov multi-dimensional almost periodic functions and applications

Abstract

In this paper, we analyze several various classes of Stepanov multi-dimensional almost periodic functions in Lebesgue spaces with variable exponents. The introduced classes seem to be new and not considered elsewhere even in the case that the exponent $p(\cdot)$ has a constant value. We provide certain applications to the abstract (degenerate) Volterra integro-differential equations in Banach spaces.