J. Nonl. Evol. Equ. Appl. 2023 (3), pp. 35-52, published on July 10, 2023:

Besicovitch multi-dimensional almost automorphic type functions and applications

Marko Kostić

Faculty of Technical Sciences, University of Novi Sad, Trg D. Obradovica 6, 21125 Novi Sad, Serbia

Received on March 4, 2022, Revised on March 11, 2023
Accepted with modifications on February 20, 2023, final version on March 11, 2023

Communicated by Gaston M. N'Guérékata

Abstract.  In this paper, we introduce in a natural way a new class of (ω, c)-periodic functions and investigate some of their properties. We prove that the set of such functions is a Banach space under an appropriate norm and provide a composition result. We give also several examples of such functions.
Keywords: Besicovitch almost automorphic functions in Rn, Besicovitch almost periodic functions in Rn, Weyl almost automorphic functions in Rn, Lebesgue spaces with variable exponents, abstract Volterra integro-differential equations.
2010 Mathematics Subject Classification:   42A75, 43A60, 47D99.

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