Uniformly continuos superposition operators on spaces of functions of bounded variation defined on compact subset of C

Abstract

In this paper we show that if the generating function h, of a uniformly continuous superposition operator H, is continuous in the first variable and if H sends a range-restricted subset of BV (σ), the space of functions of bounded variation on compact subset σ ⊂ C, into another such space, then the function h must be affine in the functional (second) variable.