Asymptotically Weyl almost periodic functions in Lebesgue spaces with\n variable exponents

2020/01/19 by Marko Kostić, Kostić, Marko
Engineering · Mathematics · #Differential Equations and Boundary Problems #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Differential Equations Analysis #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2001.08080

openalex publication_date 2020/01/19 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

In this paper, we introduce and analyze several different notions of Weyl\nalmost periodic functions and Weyl ergodic components in Lebesgue spaces with\nvariable exponent L^p(x). We investigate the invariance of (asymptotical)\nWeyl almost periodicity with variable exponent under the actions of convolution\nproducts, providing also some illustrative applications to abstract fractional\ndifferential inclusions in Banach spaces. The introduced classes of generalized\n(asymptotically) Weyl almost periodic functions are new even in the case that\nthe function p(x) has a constant value p\≥ 1, provided that the functions\n\φ(x) and F(l,t) under our consideration satisfy \φ(x)\≠ x or\nF(l,t)\≠ l^(-1)/p.\n

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