On Calderon's Conjecture

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. Unlike the case of the bilinear Hilbert transform, a more singular operator not covered by the Calderón-Zygmund theory, the boundeness of Calderón-Zygmund operators on the full range of exponents is known.…”

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…”

L p estimates for the biest II. The Fourier case

“…From the work of Lacey and Thiele [13], [14] we have the following L p estimates on B: Theorem 1.1. B maps L p × L q → L r whenever 1 < p, q ≤ ∞, 1/p + 1/q = 1/r, and 2/3 < r < ∞.…”