Abstract
The convex body maximal operator is a natural generalization of the Hardy–Littlewood maximal operator. In this paper we are considering its dyadic version in the presence of a matrix weight. To our surprise it turns out that this operator is not bounded. This is in a sharp contrast to a Doob's inequality in this context. At first, we show that the convex body Carleson Embedding Theorem with matrix weight fails. We then deduce the unboundedness of the matrix-weighted convex body maximal operator.
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