Fractional Navier–Stokes equations and a Hölder-type inequality in a sum of singular spaces

In this paper we study the local well-posedness of the fractional Navier–Stokes system with initial data belonging to a sum of two pseudomeasure-type spaces denoted by PMa,b:=PMa+PMbPMa,b:=PMa+PMb. The proof requires showing a Hölder-type inequality in PMa,bPMa,b, as well as establishing estimates of the semigroup generated by the fractional power of Laplacian (−Δ)γ(−Δ)γ on these spaces.