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1. CMB 2000 (vol 43 pp. 330)
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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 |