Reiteration formulae for interpolation methods associated to polygons

Abstract

We study spaces generated by applying the interpolation methods defined by a polygon Π to an N-tuple of real interpolation spaces with respect to a fixed Banach couple {X, Y }. We show that if the interior point (α,β) of the polygon does not lie in any diagonal of Π then the interpolation spaces coincide with sums and intersections of real interpolation spaces generated by {X, Y }. Applications are given to N-tuples formed by Lorentz function spaces and Besov spaces. Moreover, we show that results fail in general if (α,β) is in a diagonal.