Recent progress on the Kakeya conjecture.
We survey recent developments on the Kakeya problem. [Proceedings of the 6th International Conference on Harmonic Analysis and Partial Differential Equations, El Escorial (Madrid), 2002].
Matrix Valued Paraproducts.
Elementary proofs and the sums differences problem.
In this paper, we rule out the possibility that a certain method of proof in the sums differences conjecture can settle the Kakeya Conjecture.
On the self crossing six sided figure problem.
Pseudodifferential Operators on SU(2).
On the two weights problem for the Hilbert transform.
In this paper, we prove sufficient conditions on pairs of weights (u,v) (scalar, matrix or operator valued) so that the Hilbert transform H f(x) = p.v. ∫ [f(y) / x - y] dy, is bounded from L2(u) to L2(v).
Some connections between Falconer's distance set conjecture and sets of Furstenburg type.
Checkerboards, Lipschitz functions and uniform rectifiability.
In his recent lecture at the International Congress [S], Stephen Semmes stated the following conjecture for which we provide a proof.
An improved bound on the Minkowski dimension of Besicovitch sets in .
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