Multilinear square functions and multiple weights

Abstract

In this paper we prove weighted estimates for a class of smooth multilinear square functions with respect to multilinear $A_{\vec P}$ weights. In particular, we establish weighted estimates for the smooth multilinear square functions associated with disjoint cubes of equivalent side-lengths. As a consequence, for this particular class of multilinear square functions, we provide an affirmative answer to a question raised by Benea and Bernicot (Forum Math. Sigma 4, 2016, e26) about unweighted estimates for smooth bilinear square functions.

Sharp maximal estimates for multilinear commutators of multilinear strongly singular Calderón–Zygmund operators and applications

“…Si and Xue [22] proved weighted norm inequalities for multilinear square functions with kernels of Dini's type with A ⃗ p weights. For related research on the theory of multilinear square functions, one can see [3,4,5,8]…”