Geodesic
Maximal Operators and Cantor Sets
Canadian mathematical bulletin, Tome 43 (2000) no. 3, pp. 330-342

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DOI

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.
DOI : 10.4153/CMB-2000-040-5
Mots-clés : 42B25, 43A46, maximal function, Cantor set, lacunary set 
Hare, Kathryn E. Maximal Operators and Cantor Sets. Canadian mathematical bulletin, Tome 43 (2000) no. 3, pp. 330-342. doi: 10.4153/CMB-2000-040-5
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     author = {Hare, Kathryn E.},
     title = {Maximal {Operators} and {Cantor} {Sets}},
     journal = {Canadian mathematical bulletin},
     pages = {330--342},
     year = {2000},
     volume = {43},
     number = {3},
     doi = {10.4153/CMB-2000-040-5},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2000-040-5/}
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