On a class of (non)local superposition operators of arbitrary order

Abstract In this paper we introduce a very general setting dealing with the superposition of operators of any positive order and provide a systematic study of them. We also provide examples and counterexamples, as well as characterizing properties of the measures and the functional spaces under consideration (these features are of special importance, since they delineate the boundaries of a general theory). Moreover, we present some applications regarding the existence theory for a class of nonlinear problems involving superposition operators of arbitrary (possibly fractional) order.