Composing functions of bounded Korenblum variation. (English) Zbl 1300.47071
Summary: We prove that the autonomous composition operator \(Hf=h\circ f\) maps the space \(\kappa BV\) of all functions of bounded Korenblum variation into itself if and only if the generating function \(h\) is locally Lipschitz on the real line.
MSC:
47H30 | Particular nonlinear operators (superposition, Hammerstein, Nemytskiĭ, Uryson, etc.) |
26A45 | Functions of bounded variation, generalizations |