ar X iv : m at h / 99 06 09 7 v 2 [ m at h . C O ] 3 1 A ug 1 99 9 BOUNDS ON ARITHMETIC PROJECTIONS , AND APPLICATIONS TO THE KAKEYA CONJECTURE
نویسنده
چکیده
Let A, B, be finite subsets of an abelian group, and let G ⊂ A × B be such that #A, #B, #{a + b : (a, b) ∈ G} ≤ N. We consider the question of estimating the quantity #{a − b : (a, b) ∈ G}. In [2] Bourgain obtained the bound of N 2− 1 13 , and applied this to the Kakeya conjecture. We improve Bourgain's estimate to N
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