Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bounds for Kakeya-type maximal operators associated with k-planes   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 (d,k) set has positive Lebesgue measure. We give
a short proof of this result which allows for an improved L^p estimate of the
corresponding maximal operator, and which demonstrates that a lower value of
k_{cr} could be obtained if improved mixed-norm estimates for the x-ray
transform were known.

1
The categories of this paper are: cs
36
The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an
17
The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
13
The categories of this paper are: quant-ph
15
The categories of this paper are: nucl-ex
27
The categories of this paper are: comp-gas
32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat
9
The categories of this paper are: nlin
28
The categories of this paper are: alg-geom
18
The categories of this paper are: econ