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Tuesday, May 04, 2021
11:00 AM - 11:50 AM
Online Event

Caltech/UCLA Joint Analysis Seminar

The matrix-weighted Hardy-Littlewood maximal function is unbounded
Stefanie Petermichl, Departement de Mathematiques, Universite Paul Sabatier, Toulouse,


In a joint work with Nazarov, Skreb and Treil, we highlight a marked difference in the presence of a matrix weight between the Doob type maximal operator in the dyadic setting (with absolute values outside) and the dyadic Hardy-Littlewood type maximal operator (with absolute values inside). The former is L2 bounded while the latter is not. 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.

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