Nonlinear composition operators in bv_p spaces: continuity and compactness

TL;DR

This paper investigates the continuity and compactness properties of nonlinear composition operators on sequence spaces of bounded variation, extending previous work and providing comprehensive characterizations of various continuity types.

Contribution

It offers new characterizations of multiple continuity and compactness properties of nonlinear composition operators on bv_p spaces.

Findings

Characterization of pointwise, uniform, and locally uniform continuity

Analysis of Lipschitz and Hölder continuity properties

Criteria for compactness of composition operators

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 H\"older continuity. Furthermore, we provide a characterization of the compactness properties of these operators.