Functions of bounded variation from ideal perspective

TL;DR

This paper introduces a unified framework for analyzing Waterman spaces and Chanturia classes, two types of Banach spaces characterized by variations, using concepts from the theory of ideals on natural numbers.

Contribution

It provides a novel ideal-based approach to study the structure of these variation-based Banach spaces, unifying their analysis.

Findings

Unified approach to Waterman and Chanturia spaces

New insights into the structure of variation-based Banach spaces

Potential applications to functional analysis and space classification

Abstract

We present a unified approach to two classes of Banach spaces defined with the aid of variations: Waterman spaces and Chanturia classes. Our method is based on some ideas coming from the theory of ideals on the set of natural numbers.