Multi-dimensional Weyl almost periodic type functions and applications

TL;DR

This paper introduces new classes of multi-dimensional Weyl almost periodic functions in Lebesgue spaces with variable exponents and explores their applications to abstract Volterra integro-differential equations.

Contribution

It presents novel classes of Weyl almost periodic functions in variable exponent Lebesgue spaces, not previously studied even in constant coefficient cases.

Findings

New classes of Weyl almost periodic functions introduced

Applications to Volterra integro-differential equations demonstrated

Potential for further research in variable exponent spaces

Abstract

In this paper, we analyze multi-dimensional Weyl almost periodic type functions in Lebesgue spaces with variable exponents. The introduced classes seem to be new and not considered elsewhere even in the constant coefficient case. We provide certain applications to the abstract Volterra integro-differential equations in Banach spaces.