Inclusion of $\Lambda^{\#} BV^{(p)}$ spaces in the classes $BV(q(n)\uparrow \infty)$

TL;DR

This paper investigates the inclusion relationships between multivariable Waterman-Shiba classes and variable exponent bounded variation classes, providing characterizations of when one class is contained within the other.

Contribution

It introduces multivariable Waterman-Shiba classes and $BV(q(n) o\infty)$ classes, and characterizes their inclusion relations, extending classical function space theory.

Findings

Characterization of inclusion conditions between classes

Introduction of multivariable Waterman-Shiba classes

Extension of bounded variation classes to variable exponents

Abstract

The multivariable version of Waterman-Shiba classes and $BV(q(n)\uparrow \infty)$ are introduced. Also characterization of the inclusion of multivariable Waterman-Shiba classes into classes of functions multivariable $BV(q(n)\uparrow \infty)$ is given.