Canad. Math. Bull. 43(2000), 330-342
Printed: Sep 2000
We consider maximal operators in the plane, defined by Cantor sets of
directions, and show such operators are not bounded on $L^2$ if the
Cantor set has positive Hausdorff dimension.
maximal functions, Cantor set, lacunary set
42B25 - Maximal functions, Littlewood-Paley theory
43A46 - Special sets (thin sets, Kronecker sets, Helson sets, Ditkin sets, Sidon sets, etc.)