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- W2031037583 abstract "Let $m ge 2$ and define the multilinear Littlewood–Paley $g$-function by $$g(vec{f})(x)=bigg(int_{0}^{infty} bigg| frac{1}{t^{mn}}int_{(mathbb{R}^n)^m} psibigg(frac{y_1}{t},dots,frac{y_m}{t}bigg) prod_{j=1}^mf_j(x-y_j)dy_{j}bigg|^2 frac{dt}{t} bigg)^{1/2}.$$ In this paper, we establish the strong $L^{p_1}(w_1)times dots times L^{p_m}(w_m)$ to $L^p(nu_{vec{omega}}$) boundedness and weak type $L^{p_1}(w_1)times dots times L^{p_m}(w_m)$ to $L^{p,infty}(nu_{vec{omega}}$) estimate for the multilinear $g$-function. The weighted strong and end-point estimates for the iterated commutators of $g$-function are also given. Here $nu_{vec{omega}} = prod_{i = 1}^momega_i^{{p}/{p_i}}$ and each $w_i$ is a nonnegative function on $mathbb{R}^n$." @default.
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- W2031037583 date "2015-04-01" @default.
- W2031037583 modified "2023-09-27" @default.
- W2031037583 title "On the theory of multilinear Littlewood–Paley $g$-function" @default.
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- W2031037583 doi "https://doi.org/10.2969/jmsj/06720535" @default.
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