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Search: MSC category 43A46 ( Special sets (thin sets, Kronecker sets, Helson sets, Ditkin sets, Sidon sets, etc.) )

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1. CMB 2000 (vol 43 pp. 330)

Hare, Kathryn E.
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
Categories:42B25, 43A46

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