Martingale transforms, the dyadic shift and the Hilbert transform: a sufficient condition for boundedness between matrix weighted spaces

Details Martingale transforms, the dyadic shift and the Hilbert transform: a sufficient condition for boundedness between matrix weighted spaces Martingale transforms, the dyadic shift and the Hilbert transform: a sufficient condition for boundedness between matrix weighted spaces

2009-06-22

arxiv.org/abs/0906.4028v4

Mathematics

Classical Analysis and ODEs

15 pages, 2 figures

Scientific paper

We show sufficient conditions on matrix weights $U$ and $V$ for the
martingale transforms to be uniformly bounded from $L^2(V)$ to $L^2(U)$. We
also show that these conditions imply the uniform boundedness of the dyadic
shifts as well as the boundedness of the Hilbert transform between these
spaces.

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