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• W3180365685 abstract "Let $$S_{alpha }$$ be the multilinear square function defined on the cone with aperture $$alpha ge 1$$ . In this paper, we investigate several kinds of weighted norm inequalities for $$S_{alpha }$$ . We first obtain a sharp weighted estimate in terms of aperture $$alpha $$ and $$vec {w} in A_{vec {p}}$$ . By means of some pointwise estimates, we also establish two-weight inequalities including bump and entropy bump estimates, and Fefferman–Stein inequalities with arbitrary weights. Beyond that, we consider the mixed weak type estimates corresponding Sawyer’s conjecture, for which a Coifman–Fefferman inequality with the precise $$A_{infty }$$ norm is proved. Finally, we present the local decay estimates using the extrapolation techniques and dyadic analysis respectively. All the conclusions aforementioned hold for the Littlewood–Paley $$g^*_{lambda }$$ function. Some results are new even in the linear case." @default.
• W3180365685 created "2021-07-19" @default.
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• W3180365685 date "2021-07-09" @default.
• W3180365685 modified "2023-10-11" @default.
• W3180365685 title "Weak and Strong Type Estimates for the Multilinear Littlewood–Paley Operators" @default.
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• W3180365685 doi "https://doi.org/10.1007/s00041-021-09870-x" @default.
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