Mathematical Research Letters

Volume 3 (1996)

Number 4

A counterexample for maximal operators over a Cantor set of directions

Pages: 527 – 536

DOI: http://dx.doi.org/10.4310/MRL.1996.v3.n4.a10

Author

Nets Hawk Katz (Yale University)

Abstract

We produce a counterexample to the boundedness of the Cantor set maximal operator. We also produce a sharp counterexample for the restriction of the maximal operator of a truncated Cantor set to a strip.

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