New uniform bounds for a Walsh model of the bilinear Hilbert transform

Details New uniform bounds for a Walsh model of the bilinear Hilbert transform New uniform bounds for a Walsh model of the bilinear Hilbert transform

2010-04-22

arxiv.org/abs/1004.4019v1

Mathematics

Classical Analysis and ODEs

19 pages

Scientific paper

We prove old and new $L^p$ bounds for the quartile operator, a Walsh model of the bilinear Hilbert transform, uniformly in the parameter that models degeneration of the bilinear Hilbert transform. We obtain the full range of exponents that can be expected from known bounds in the degenerate and non-degenerate cases. For the new estimates with exponents p close to 1 the argument relies on a multi-frequency Calderon-Zygmund decomposition.

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