A simple characterization of $H$-convergence for a class of nonlocal problems

This is a follow-up of a paper by Fern'andez-Bonder-Ritorto-Salort [8], where the classical concept of $H$-convergence was extended to fractional $p$-Laplace type operators. In this short paper we provide an explicit characterization of this notion by demonstrating that the weak-* convergence of the coefficients is an equivalent condition for $H$-convergence of the sequence of nonlocal operators. This result takes advantage of nonlocality and is in stark contrast to the local p-Laplacian case