1 5 N ov 2 00 7 Dimension free bilinear embedding and Riesz transforms associated with the

N ov 2 00 8 Linear dimension - free estimates for the Hermite - Riesz transforms ∗ Oliver Dragičević and Alexander Volberg

We utilize the Bellman function technique to prove a bilinear dimension-free inequality for the Hermite operator. The Bellman technique is applied here to a non-local operator, which at first did not seem to be feasible. As a consequence of our bilinear inequality one proves dimension-free boundedness for the Riesz-Hermite transforms on L with linear growth in terms of p. A feature of the proof...

N ov 2 00 4 L p - estimates for Riesz transforms on forms in the Poincaré space

Using hyperbolic form convolution with doubly isometry-invariant kernels, the explicit expression of the inverse of the de Rham laplacian ∆ acting on m-forms in the Poincaré space H is found. Also, by means of some estimates for hyperbolic singular integrals, L-estimates for the Riesz transforms ∇i∆−1, i ≤ 2, in a range of p depending on m,n are obtained. Finally, using these, it is shown that ...

ar X iv : 0 81 1 . 28 54 v 1 [ m at h . FA ] 1 8 N ov 2 00 8 L p estimates for non smooth bilinear Littlewood - Paley square functions

L p estimates for non smooth bilinear Littlewood-Paley square functions on R. Abstract In this work, some non smooth bilinear analogues of linear Littlewood-Paley square functions on the real line are studied. Mainly we prove boundedness-properties in Lebesgue spaces for them. Let us consider the function φn satisfying c φn(ξ) = 1 [n,n+1] (ξ) and consider the bilinear operator Sn(f, g)(x) := R ...

1 7 N ov 2 00 4 Cosine Products , Fourier Transforms , and Random Sums ∗

ar X iv : m at h / 05 09 09 7 v 2 [ m at h . G N ] 1 5 N ov 2 00 5 COSMIC DIMENSIONS

Martin's Axiom for σ-centered partial orders implies that there is a cosmic space with non-coinciding dimensions.