Wavelet expansions for weighted, vector-valued BMO functions

TL;DR

This paper develops a framework connecting weighted BMO functions and wavelet coefficients via Carleson norms, extending classical results to vector-valued functions and different integrability parameters.

Contribution

It introduces a new scale of weighted Carleson norms depending on p, and establishes relations between these norms and wavelet coefficients for vector-valued BMO functions.

Findings

Extended classical Carleson measure results to weighted, vector-valued functions.

Established relations between BMO norms and wavelet coefficient norms.

Generalized results to non-2 integrability parameters p.

Abstract

We introduce a scale of weighted Carleson norms, which depend on an integrability parameter p, where p=2 corresponds to the classical Carleson measure condition. Relations between the weighed BMO norm of a vector-valued function f:R->X, and the Carleson norm of the sequence of its wavelet coefficients, are established. These extend the results of Harboure-Salinas-Viviani, also in the scalar-valued case when p is not 2.