Vertical versus conical square functions

TL;DR

This paper investigates the differences between vertical and conical square functions both generally and specifically in the context of elliptic operators, aiming to clarify their distinct behaviors and relationships.

Contribution

It provides a comparative analysis of vertical and conical square functions, including new insights in the setting of elliptic operators.

Findings

Identifies key differences between vertical and conical square functions.

Establishes conditions under which the two types of square functions are comparable.

Provides examples illustrating the divergence in their behaviors.

Abstract

We study the difference between vertical and conical square functions in the abstract and also in the specific case where the square functions come from an elliptic operator.