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# Maximal Operators and Cantor Sets

Published:2000-09-01
Printed: Sep 2000
• Kathryn E. Hare
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## Abstract

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
 MSC Classifications: 42B25 - Maximal functions, Littlewood-Paley theory 43A46 - Special sets (thin sets, Kronecker sets, Helson sets, Ditkin sets, Sidon sets, etc.)