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

In this paper we give sufficient conditions on k is an element of L-1(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 * 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 (mu, nu)-pseudo-almost periodic (respectively, (mu, nu)-pseudo-almost automorphic) solutions to some nonautonomous partial evolution equations in Banach spaces like neutral systems.