The dyadic and the continuous Hilbert transforms with values in Banach spaces. Part2
Functional Analysis
2023-03-23 v1 Probability
Abstract
We show that if the dyadic Hilbert transform with values in a Banach space is bounded, then so is the Hilbert transform, with a linear relation of the bounds. This result is the counterpart of [arXiv:2212.00090] where the opposite bound was proven.
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Cite
@article{arxiv.2303.12480,
title = {The dyadic and the continuous Hilbert transforms with values in Banach spaces. Part2},
author = {Komla Domelevo and Stefanie Petermichl},
journal= {arXiv preprint arXiv:2303.12480},
year = {2023}
}
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19 pages