On General multilinear square function with non-smooth kernels

Abstract

In this paper, we obtain some boundedness of the following general multilinear square functions $T$ with non-smooth kernels, which extend some known results significantly. $$T(\vec{f})(x)=\left({\int }_0^{\infty }\right|{\int }_{({\mathbb{R}}^n{)}^m}{K}_v(x,y_1,\dots ,y_m)\prod _{j=1}^m{f}_j(y_j)d{y}_1,\dots ,d{y}_m{|}^2\frac{dv}{v}{)}^{\frac{1}{2}}.$$ The corresponding multilinear maximal square function $T^{\ast }$ was also introduced and weighted strong and weak type estimates for $T^{\ast }$ were given.

19 pages