A new type of superorthogonality

TL;DR

This paper introduces a novel, less restrictive form of superorthogonality that ensures square function estimates on L^p spaces for all even p ≥ 2, broadening the scope of applicable function families.

Contribution

It proposes a new, simpler criterion for superorthogonality that guarantees square function estimates across all even L^p spaces, expanding theoretical understanding.

Findings

New superorthogonality criterion established

Ensures square function estimates for all even p ≥ 2

Less restrictive than existing superorthogonality types

Abstract

We provide a simple criterion on a family of functions that implies a square function estimate on $L^p$ for every even integer $p \geq 2$. This defines a new type of superorthogonality that is verified by checking a less restrictive criterion than any other type of superorthogonality that is currently known.