In this work, quantitative structure-property relationship (QSPR) approaches were used to predict the redox potential of 42 phenolic antioxidants. The structures of all compounds optimized by the AM1 semi-empirical method and then a large number of molecular descriptors were calculated for each compound in the data set. Subsequently, stepwise multilinear regression was applied to select the mos...

A new proof of a weighted norm inequality for multilinear singular integrals of Calderón-Zygmund type is presented through a more general estimate involving a sharp maximal function. An application is given to the study of certain multilinear commutators.

A multilinear version of the Boyd interpolation theorem is proved in the context of quasi-normed rearrangement-invariant spaces. A multilinear Marcinkiewicz interpolation theorem is obtained as a corollary. Several applications are given, including estimates for bilinear fractional integrals.

We extend the well-known Shannon decomposition of Boolean functions to more general classes of functions. Such decompositions, which we call pivotal decompositions, express the fact that every unary section of a function only depends upon its values at two given elements. Pivotal decompositions appear to hold for various function classes, such as the class of lattice polynomial functions or the...

A new characterization of the Dunford-Pettis property in terms of the extensions of multilinear operators to the biduals is obtained. For the first time, multilinear characterizations of the reciprocal Dunford-Pettis property and Pe lczyński’s property (V) are also found. Polynomial and holomorphic versions of these properties are given as well.

We prove that mutlilinear paraproducts are bounded from products of Lebesgue spaces L1 ×· · ·×Lm+1 to Lp,∞, when 1 ≤ p1, . . . , pm+1 <∞, 1/p1+· · ·+1/pm+1 = 1/p. We focus on the endpoint case when some indices pj are equal to 1, in particular we obtain the new endpoint estimate L× · · · ×L → L1/(m+1),∞. In memory of Nigel Kalton

In this paper, we prove some uniform estimates between Lebesgue and Hardy spaces for operators closely related to the multilinear paraproducts on Rd. We are looking for uniformity with respect to parameters, which allow us to disturb the geometry and the metric on Rd.

The construction of cryptographic multilinear maps and a general-purpose code obfuscator were two long-standing open problems in cryptography. It has been clear for a number of years that constructions of these two primitives would yield many interesting applications. This thesis describes the Coron-Lepoint-Tibouchi candidate construction for multilinear maps, as well as new candidates for code...

The multilinear Calderón–Zygmund theory is developed in the setting of RD-spaces, namely, spaces of homogeneous type equipped with measures satisfying a reverse doubling condition. The multiple-weight multilinear Calderón–Zygmund theory in this context is also developed in this work. The bilinear T1-theorems for Besov and Triebel–Lizorkin spaces in the full range of exponents are among the main...

We introduce the concept of multilinear partition of a point set V/spl sub/R/sup n/ and the concept of multilinear separability of a function f:Vtwo head right arrowK={0,...,k-1}. Based on well-known relationships between linear partitions and minimal pairs, we derive formulae for the number of multilinear partitions of a point set in general position and of the set K(2). The (n,k,s)-perceptron...