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.
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).
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.
On the self crossing six sided figure problem.
Some connections between Falconer's distance set conjecture and sets of Furstenburg type.
An improved bound on the Minkowski dimension of Besicovitch sets in .
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