Search: MSC category 43A46
( Special sets (thin sets, Kronecker sets, Helson sets, Ditkin sets, Sidon sets, etc.) )
1. CMB 2000 (vol 43 pp. 330)
||Maximal Operators and Cantor Sets |
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.
Keywords:maximal functions, Cantor set, lacunary set