Resumen de Maximal operators and Hilbert transforms along flat curves near L1

Neal Bez

• For a class of convex curves in Rd we prove that the corresponding maximal operator and Hilbert transform are of weak type Llog L. The point of interest here is that this class admits curves which are infinitely flat at the origin. We also prove an analogous weak type result for a class of nonconvex hypersurfaces.