Let P→ = (p1, … , pm) with 1 < p1, …, pm < ∞, 1/p1+⋯+1/pm=1/p and w→ = (w1, … , wm) ∈ AP→. In this paper, we investigate the weighted bounds with dependence on aperture α for multilinear square functions Sα,ψ(f→ ). We show that (Formula presented.). This result extends the result in the linear case which was obtained by Lerner in 2014. Our proof is based on the local mean oscillation technique presented firstly to find the weighted bounds for Calderón–Zygmund operators. This method helps us avoiding intrinsic square functions in the proof of our main result.
- Multilinear singular integrals
- Weighted norm inequalities
- Aperture dependence