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math.FA2022
The dyadic and the continuous Hilbert transforms with values in Banach spaces
Komla Domelevo, Stefanie Petermichl
We show that if the Hilbert transform with values in a Banach space is bounded, then so is the dyadic Hilbert transform, with a linear relation of the norms.
math.FA2022
The matrix-weighted dyadic convex body maximal operator is not bounded
F. Nazarov, S. Petermichl, K. A. Škreb +1
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.