Schramm spaces and composition operators

Abstract

. We give some properties of Schramm functions; among others, we prove that the family of all continuous piecewise linear functions defined on a real interval I is contained in the space Φ BV ( I ) of functions of bounded variation in the sense of Schramm. Moreover, we show that the generating function of the corresponding Nemytskij composition operator acting between Banach spaces C Φ BV ( I ) of continuous functions of bounded Schramm variation has to be continuous and additionally we show that a space C Φ BV ( I ) has the Matkowski property.