On the theory of multilinear Littlewood–Paley <i>g</i>-function

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  • Xue Qingying
    School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education
  • Peng Xiuxiang
    School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education
  • Yabuta Kôzô
    Research Center for Mathematical Sciences, Kwansei Gakuin University

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  • On the theory of multilinear Littlewood-Paley g-function

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Let m ≥ 2 and define the multilinear Littlewood–Paley g-function by<img align="middle" src="./Graphics/abst-535.jpg"/>In 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.

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