Caltech/UCLA Joint Analysis Seminar

PLEASE NOTE DIFFERENT TIME

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.