Convolutions in (µ, ν)-pseudo-almost periodic and (µ, ν)-pseudo-almost automorphic function spaces and applications to solve integral equations

• Main Authors: David Békollè, Khalil Ezzinbi, Samir Fatajou, Duplex Elvis Houpa Danga, Fritz Mbounja Béssémè
• Format: Article
• Language: English
• Published: Universidad de La Frontera 2021-04-01
• Series: Cubo
• Subjects: measure theory; μ-ν-ergodic; μ-ν -pseudo almost periodic and automorphic functions; evolution families; nonautonomous equations; neutral systems
• Online Access: http://revistas.ufro.cl/ojs/index.php/cubo/article/view/2598/2052
• ISSN: 0716-7776; 0719-0646

In this paper we give sufficient conditions on $k\in L^1(\mathbb{R})$ and the positive measures $\mu$, $\nu$ such that the doubly-measure pseudo-almost periodic (respectively, doubly-measure pseudo-almost automorphic) function spaces are invariant by the convolution product $\zeta f=k\ast f$. We provide an appropriate example to illustrate our convolution results. As a consequence, we study under Acquistapace-Terreni conditions and exponential dichotomy, the existence and uniqueness of $\left( \mu,\nu\right)$- pseudo-almost periodic (respectively, $\left( \mu,\nu\right)$- pseudo-almost automorphic) solutions to some nonautonomous partial evolution equations in Banach spaces like neutral systems.