On the theory of multilinear Littlewood–Paley g-function

抄録

Let m ≥ 2 and define the multilinear Littlewood–Paley g-function byIn this paper, we establish the strong Lp1(w1) × ⋯ × Lpm(wm) to Lp(ν\vec{ω}) boundedness and weak type Lp1(w1) × ⋯ × Lpm(wm) to Lp,∞(ν\vec{ω}) estimate for the multilinear g-function. The weighted strong and end-point estimates for the iterated commutators of g-function are also given. Here ν\vec{ω} = ∏mi=1ωp/pii and each wi is a nonnegative function on ℝn.