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A maximal function for families of Hilbert transforms along homogeneous curves

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ASC - Approximation, sampling and compression in data science

Let H(u) be the Hilbert transform along the parabola (t; ut2) where u 2 R. For a set U of positive numbers consider the maximal function HUf = supfH(u)f : u 2 Ug. We obtain (essentially) optimal results for the
Lp operator norm of HU when 2 < p < 1. The results are proved for families of Hilbert transforms along more general non- at homogeneous curves. Joint work with Shaoming Guo, Joris Roos and Po-Lam Yung.

This talk is part of the Isaac Newton Institute Seminar Series series.

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