Nonlinear composition operators in bv_p spaces: continuity and compactness

Abstract

Continuing the study initiated in our earlier article [7], this paper aims to characterize various continuity properties of nonlinear composition operators acting on some sequence spaces, giving special attention to the space of sequences of bounded variation. In addition to pointwise, uniform, and locally uniform continuity, we investigate Lipschitz continuity as well as several types of Hölder continuity. Furthermore, we provide a characterization of the compactness properties of these operators.

46 pages