Commutateurs d'intégrales singulières et opérateurs multilinéaires

Minimal regularity conditions for the end-point estimate of bilinear Calderón-Zygmund operators

“…Under regularity assumptions analogous to (1.1) or (1.2), the theory has been developed through works of Coifman-Meyer [2], [3], [4], Christ-Journé [6], Kenig-Stein [15] and Grafakos-Torres [10], [11]. Some of the most recent work in the subject was motivated in part by the results of Lacey-Thiele [16], [17] on the bilinear Hilbert transform and a search for the optimal range of exponents where boundedness in Lebesgue spaces can be obtained.…”

The Hörmander multiplier theorem for multilinear operators

“…In this article, we provide a version of the Hörmander multiplier theorem in the case of multilinear operators. The study of such operators originated in the work of Coifman and Meyer [2], [3], [4] and was later revived by the groundbreaking work of Lacey and Thiele's on the bilinear Hilbert transform [12], [13]. The multilinear Fourier multiplier operator T σ associated with a symbol σ is defined by…”

On multilinear singular integrals of Calderón-Zygmund type

“…Their study is also motivated by many linear and nonlinear problems in which multilinear operators naturally appear as terms of series expansions. This last point of view was pioneered and extensively pursued by Coifman and Meyer in [13], [14], [15], [16], and [47]. See also the work of Coifman, Deng, and Meyer [8], Fabes, Jerison, and Kenig [21], and Christ and Kiselev [7] where multilinear operators are used in the study of specific problems in partial differential equations.…”