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math.CA2005★ 2 cited
Bounds for Kakeya-type maximal operators associated with k-planes
Richard Oberlin
A (d,k) set is a subset of R^d containing a translate of every k-dimensional plane. Bourgain showed that for k \geq k_{cr}(d), where k_{cr}(d) solves 2^{k_{cr}-1}+k_{cr} = d, every…
math.CA2005★ 4 cited
A recursive bound for a Kakeya-type maximal operator
Richard Oberlin
A (d,k) set is a subset of R^d containing a translate of every k-dimensional plane. Bourgain showed that for 2^{k-1}+k \geq d, every (d,k) set has positive Lebesgue measure. We giv…