4 citations · 9 across the 3 of their papers we have counts for
3 papers
math.CA2008★ 4 cited
An estimate from below for the Buffon needle probability of the four-corner Cantor set
Michael Bateman, Alexander Volberg
Let $\Cant_n$ be the -th generation in the construction of the middle-half Cantor set. The Cartesian square $\K_n = \Cant_n \times \Cant_n$ consists of squares of side-len…
math.CA2008★ 2 cited
L^p Estimates for Maximal Averages Along One-variable Vector Fields in R^2
Michael Bateman
We prove a conjecture of Lacey and Li in the case that the vector field depends only on one variable. Specifically: let v be a vector field defined on the unit square such that v(x…
math.CA2007★ 3 cited
Kakeya Sets and Directional Maximal Operators in the Plane
Michael Bateman
We completely characterize the boundedness of planar directional maximal operators on L^p. More precisely, if Omega is a set of directions, we show that M_Omega, the maximal operat…