The dyadic Riesz vector I

TL;DR

This paper introduces a dyadic model operator for the Riesz vector and establishes linear lower bounds in L^p spaces, linking the model's boundedness to that of the Riesz vector in Banach space-valued functions.

Contribution

It constructs a dyadic Riesz vector model and proves lower bounds that connect its boundedness to the classical Riesz vector in Banach space contexts.

Findings

Established linear lower L^p bounds for the dyadic Riesz vector model

Linked the boundedness of the model to the classical Riesz vector

Extended results to functions with values in Banach spaces

Abstract

We derive a dyadic model operator for the Riesz vector. We show linear lower $L^p$ bounds for $1 < p < \infty$ between this model operator and the Riesz vector, when applied to functions with values in Banach spaces. By a lower bound we mean that the boundedness of the Riesz vector implies the boundedness of the dydic Riesz vector.