Dr Jacek Gulgowski

(Institute of Mathematics, GdaĆsk University)**On the continuity of superposition operator in the spaces of functions of bounded variation**

It is a well-know fact that the superposition of a function satisfying a local Lipschitz condition with a function of bounded variation leads to the function which is also of bounded variation. During the seminar we are going to present a few results concerning the continuity of such a superposition operator . Furthermore, we are going to discuss several generalizations of the concept of bounded variation in the sense of Jordan and investigate the issue of continuity of the superposition operator , where denotes the space of functions of bounded variation in the generalized sense.