Joint BCAM-UPV/EHU Analysis and PDE seminar: The matrix-weighted Hardy-Littlewood maximal function is unbounded

Abstract
The convex body maximal operator is a natural generalisation of the Hardy-Littlewood maximal operator. In this work we are considering its dyadic version in the presence of a matrix weight. Surprisingly, it turns out that this operator is not bounded, which is in a sharp contrast to the boundedness of a Doob's inequality in this context. First, it will be discussed how to interpret these operators in a space with matrix weight. For this, we will use convex bodies to replace absolute values (equivalent to the more familiar Christ-Goldberg type definition). We will also discuss the Carleson Embedding Theorems that are the natural partners of these maximal operators and observe a different behaviour as well.

This is a joint work with F. Nazarov, S. Petermichl and S. Treil.

Link to the session: https://zoom.us/j/92839374997?pwd=Wm1DdmZzb0RIL2Z0TnpXUWUyenR3UT09

More info at https://sites.google.com/view/apdebilbao/home