New uniform bounds for a Walsh model of the bilinear Hilbert transform
Richard OberlinChristoph Thiele
42B20bilinear Hilbert transformuniform estimates
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 Calder\'on-Zygmund decomposition.
Indiana University Mathematics Journal
2011
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10.1512/iumj.2011.60.4445
10.1512/iumj.2011.60.4445
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Indiana Univ. Math. J. 60 (2011) 1693 - 1712
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