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Maximal Operators and Cantor Sets

Published online by Cambridge University Press:  20 November 2018

Kathryn E. Hare
Kathryn E. Hare*
Affiliation:
Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, N2L 3G1, email: kehare@uwaterloo.ca
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Abstract

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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

42B2543A46maximal functionCantor setlacunary set
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 43 , Issue 3 , 01 September 2000 , pp. 330 - 342
Copyright
Copyright © Canadian Mathematical Society 2000

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