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math.CA2006★ 1 cited
Two bounds for the x-ray transform
Richard Oberlin
We use the arithmetic-combinatorial method of Katz and Tao to give mixed-norm estimates for the x-ray transform on R^d when d \geq 4. As an application, we obtain an improved estim…
math.CA2005
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
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…