Bilinear Singular Integral Operators, Smooth Atoms and Molecules

Abstract

We present a bilinear T1 theorem in the context of Triebel-Lizorkin spaces. The proof uses atomic decomposition techniques and some a priori L ∞ -estimates for the action of bilinear Calderón-Zygmund operators.

On the boundedness of bilinear operators on products of Besov and Lebesgue spaces

“…for related indices p 1 , p 2 , p 3 , q 1 , q 2 , q 3 , α 1 , α 2 , α 3 , and families of bilinear operators T including bilinear multipliers, bilinear Calderón-Zygmund operators, molecular paraproducts, and bilinear pseudo-differential operators established in, for instance, [1][2][3][4][5]13,14,[16][17][18][19][20][21][22]27,29,33,34].…”

On multilinear singular integrals of Calderón-Zygmund type

“…A similar approach is feasible in the multilinear setting. Some progress in this direction has been made by Bényi [3].…”

Hardy space estimates for bilinear square functions and Calderon-Zygmund operators

“…A multilinear and multi-parameter version of the Coifman-Meyer Fourier multiplier theorem was established in [44,45] using time-frequency analysis (see also [8] using the Littlewood-Paley analysis), and a pseudo-differential analogue was carried out in [15]. There has also been some work done for the operators in the context of distributions spaces (Triebel-Lizorkin and Besov spaces), see for example [28,1,43,2]. For appropriate indices, some of these distribution spaces coincide with Hardy spaces, which are the focus of this work.…”