Multilinear square functions with kernels of Dini's type

Let t be a multilinear square function with a kernel satisfying dini(1) condition and let t∗ be the corresponding multilinear maximal square function. in this paper,first,we showed that t is bounded from l1 × ⋯ × l1 to l1/m,∞. secondly,we obtained that if each p i > 1,then t and t are bounded from lp1 (ω 1) × × lp m (ω m) to l p (ω →) and if there is pi = 1,then t and t∗ are bounded from lp1 (ω 1) × ⋯ × l p m (ω m) to lp,∞ ( ω →),where ω → = ∏i=1m ωip/pi. furthermore,we established the weighted strong and weak type boundedness for t and t on weighted morrey type spaces,respectively. © 2016 zengyan si and qingying xue.