The Favard length of product Cantor sets

Details The Favard length of product Cantor sets The Favard length of product Cantor sets

2009-02-05

arxiv.org/abs/0902.0964v1

Mathematics

Classical Analysis and ODEs

16 pages

Scientific paper

10.1112/blms/bdq059

Nazarov, Peres and Volberg proved recently that the Favard length of the
$n$-th iteration of the four-corner Cantor set is bounded from above by
$n^{-c}$ for an appropriate $c$. We generalize this result to all product
Cantor sets whose projection in some direction has positive 1-dimensional
measure.

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