The Carleson Embedding Theorem with matrix weights

TL;DR

This paper extends the Carleson Embedding Theorem to the setting of matrix weights, providing a new weighted martingale version applicable in both domain and target spaces.

Contribution

It introduces a novel matrix-weighted martingale Carleson Embedding Theorem, broadening the theorem's applicability to matrix-weighted contexts.

Findings

Proves the weighted martingale Carleson Embedding Theorem with matrix weights.

Establishes bounds for embeddings in matrix-weighted spaces.

Extends classical scalar results to matrix-valued weights.

Abstract

In this paper we prove the weighted martingale Carleson Embedding Theorem with matrix weights both in the domain and in the target space.