Boundedness of variation, oscillation and maximal differential transform on BMO space

TL;DR

This paper proves that certain operators related to oscillation, variation, and maximal differential transforms are bounded from BMO space to BLO space, advancing understanding of function space relationships.

Contribution

It establishes the boundedness of oscillation, variation, and maximal differential transform operators from BMO to BLO spaces, a novel result in harmonic analysis.

Findings

Operators are bounded from BMO to BLO spaces.

Provides new insights into the structure of BMO and BLO spaces.

Extends previous work on function space transformations.

Abstract

In this paper, we prove that the oscillation operator, variation operator and maximal differential transform associated with the approximate identities are bounded from ${\rm BMO}({\mathbb R}^n)$ to its subspace ${\rm BLO}({\mathbb R}^n)$.