Abstract:We revisit the concept of Stepanov--Orlicz almost periodic functions introduced by Hillmann in terms of Bochner transform. Some structural properties of these functions are investigated. A particular attention is paid to the Nemytskii operator between spaces of Stepanov--Orlicz almost periodic functions. Finally, we establish an existence and uniqueness result of Bohr almost periodic mild solution to a class of semilinear evolution equations with Stepanov--Orlicz almost periodic forcing term.
Keywords: Bohr almost periodic; Bochner transform; Stepanov--Orlicz almost periodic function; semilinear evolution equations; Nemytskii operator
DOI: DOI 10.14712/1213-7243.2020.030
AMS Subject Classification: 34C27 35B15 46E30