Inclusion of $\Lambda BV^{(p)}$ spaces in the classes $H_{\omega}^{q}$

TL;DR

This paper characterizes when Waterman-Shiba classes are included in classes defined by integral modulus of continuity, correcting and extending a previous 2005 result.

Contribution

It provides a new and extended characterization of the inclusion relations between Waterman-Shiba classes and classes with specified integral modulus of continuity.

Findings

Corrects a previous 2005 result on class inclusion

Extends the characterization of Waterman-Shiba class inclusion

Provides a more comprehensive understanding of function class relationships

Abstract

A characterization of the inclusion of Waterman-Shiba classes into classes of functions with given integral modulus of continuity is given. This corrects and extends an earlier result of a paper from 2005.