\documentclass[12pt]{article}
\usepackage{amsmath,amssymb,amsfonts}
\begin{document}
Let SÎ± be the multilinear square function defined on the cone with aperture Î±ï¿½?ï¿½1. In this paper, we investigate several kinds of weighted norm inequalities for SÎ±. We first obtain a sharp weighted estimate in terms of aperture Î± and wï¿½?? ï¿½??Apï¿½?? . By means of some pointwise estimates, we also establish two-weight inequalities including bump and entropy bump estimates, and Fefferman-Stein inequalities with arbitrary weights. Beyond that, we consider the mixed weak type estimates corresponding Sawyer's conjecture, for which a Coifman-Fefferman inequality with the precise Aï¿½?? norm is proved. Finally, we present the local decay estimates using the extrapolation techniques and dyadic analysis respectively. All the conclusions aforementioned hold for the Littlewood-Paley gï¿½??Î» function. Some results are new even in the linear case.
\end{document}