We show that positively 1-homogeneous rank one convex functions are convex at 0 and at
matrices of rank one. The result is a special case of an abstract convexity result that we …

This paper gives a systematic study of Sobolev, Besov and Triebel-Lizorkin spaces on a
noncommutative d-torus Td θ (with θ a skew symmetric real d× d-matrix). These spaces …

In this paper we establish an optimal Lorentz space estimate for the Riesz potential acting
on curl-free vectors: There is a constant C= C (α, d)> 0 such that‖ I α F‖ L d/(d− α), 1 (R d; …

In this paper we give a streamlined proof of an inequality recently obtained by the author:
For every aa š0, 1Ž there exists a constant C ¼ Cša, dŽ> 0 such that kukLd/šdĄaŽ, 1šRd Ž a …

Moduli, Motives, Mirrors Page 1 Moduli, Motives, Mirrors Yuri I. Manin Abstract. This talk is
dedicated to various aspects of Mirror Symmetry. It summarizes some of the mathematical …

The still image compression standard which is being developed under the name of JPEG-
2000 (Section 2) is a technological challenge which relies on some advances in pure …

In this paper we prove that every Fourier multiplier on the homogeneous Sobolev space W1
1 (Rd) is a continuous function. This theorem is a generalization of the result of A. Bonami …

One goal of these lectures is to provide you with some information about what is happening
in the still image compression standard which is devel—opped under the name of JPEG …

Munis de leur norme naturelle, ils sont tous des espaces de Banach. Les résultats obtenus
peuvent se classer en cinq familles:(i) propriétés fondamentales;(ii) caractérisations;(iii) …

Let n_j nj be a lacunary sequence of integers, such that n_ j+ 1/n_j ≥ r nj+ 1/nj≥ r. We are
interested in linear combinations of the sequence of finite Riesz products ∏ _ j= 1^ N …