A maximal function for families of Hilbert transforms along homogeneous curves
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AbstractLet H( u ) be the Hilbert transform along the parabola (t, ut2) where u∈ R. For a set U of positive numbers consider the maximal function HUf=sup{|H(u)f|:u∈U}. We obtain an (essentially) optimal result for the Lp operator norm of HU when 2 < p< ∞. The results are proved for families of Hilbert transforms along more general nonflat homogeneous curves.
All Author(s) ListShaoming Guo, Andreas Seeger, Joris Roos, Po-Lam Yung
Journal nameMathematische Annalen
Volume Number377
Issue Number1-2
Pages69 - 114
LanguagesEnglish-United States

Last updated on 2020-19-10 at 01:07