How likely is Buffon's ring toss to intersect a planar Cantor set?

Abstract: In Bateman and Volberg (2008) , it was shown that the n-th partial 1/4 Cantor in the plane set decays in Favard length no faster than . In Bond and Volberg (2008) , the so-called circular Favard length of the same set is studied, and the same estimate is shown to persist when the circle has radius . By considering characteristic functions, the result of Bond and Volberg (2008) naturally leads to a conjecture which (if true) would imply the sharpness of the boundedness of the circular maximal operator proved by Seeger, Tao and Wright (2005) . [ABSTRACT FROM AUTHOR]