Another proof of Scurry's characterization of a two weight norm inequality for a sequence-valued positive dyadic operator

TL;DR

This paper provides a new proof of Scurry's characterization of a two-weight norm inequality for a sequence-valued positive dyadic operator, using parallel stopping cubes to establish the boundedness conditions.

Contribution

It offers an alternative proof of Scurry's testing conditions for the operator's boundedness, enhancing understanding of two-weight inequalities in harmonic analysis.

Findings

Validated Scurry's testing conditions for the operator

Introduced a proof technique using parallel stopping cubes

Strengthened the theoretical framework for two-weight inequalities

Abstract

In this note we prove Scurry's testing conditions for the boundedness of a sequence-valued averaging positive dyadic operator from a weighted Lp space to a sequence-valued weighted Lp space by using parallel stopping cubes.