The matrix-weighted dyadic convex body maximal operator is not bounded

TL;DR

This paper demonstrates that the matrix-weighted dyadic convex body maximal operator, a generalization of the Hardy Littlewood maximal operator, is unbounded when matrix weights are involved.

Contribution

It provides a proof that the matrix-weighted dyadic convex body maximal operator is not bounded, highlighting limitations in extending classical boundedness results.

Findings

The operator is unbounded with matrix weights.

Classical boundedness results do not extend to this generalized setting.

The result impacts the understanding of weighted inequalities in harmonic analysis.

Abstract

The convex body maximal operator is a natural generalisation of the Hardy Littlewood maximal operator. In the presence of a matrix weight it is not bounded.