Maximal Operators and Cantor Sets

Hare, Kathryn E.

Canadian mathematical bulletin, Tome 43 (2000) no. 3, pp. 330-342

Résumé

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.

Détail

DOI : 10.4153/CMB-2000-040-5

Mots-clés : 42B25, 43A46, maximal function, Cantor set, lacunary set

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