Mathematics Dept.
University of Wisconsin-Madison
Wed 24 Apr 2019, 3:00pm
Harmonic Analysis Seminar
MATX 1102
A maximal function for families of Hilbert transforms along homogeneous curves
MATX 1102
Wed 24 Apr 2019, 3:00pm-4:00pm


Let H^(u) be the Hilbert transform along the parabola (t; ut^2).
For a set U of real numbers consider the maximal function
H^U f = sup {H^(u) f  :  u in U}.
There are sharp results for the dependence of the L^p operator norm on U when 2 < p < 1, and close to sharp results when 1 < p <= 2.
The results 
are proved for families of Hilbert transforms along more general non-flat homogeneous curves.
Joint work with Shaoming Guo, Joris Roos and Po-Lam Yung.