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- W4385348565 abstract "In this note, notwithstanding the generalization, we simplify and shorten the proofs of the main results of the third author’s paper (Shi et al in J Math Pures Appl 101:394–413, 2014) significantly. In particular, the new proof for Shi et al (J Math Pures Appl 101:394–413, 2014, Theorem 1.1) is quite short and, unlike the original proof, does not rely on the properties of the “Marcinkiewicz function”. This allows us to get a precise linear dependence on Dini constants with a subsequent application to Littlewood–Paley operators by well-known techniques. In other words, we relax the log-Dini condition in the pointwise bound to the classical Dini condition. This solves an open problem (see e.g. Cao and Yabuta in J Fourier Anal Appl 25(3):1203–1247, 2019, pp. 37–38). Our method can be applied to the multilinear case." @default.
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- W4385348565 date "2023-07-28" @default.
- W4385348565 modified "2023-10-11" @default.
- W4385348565 title "On the Weak Boundedness of Multilinear Littlewood–Paley Functions" @default.
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- W4385348565 doi "https://doi.org/10.1007/s00041-023-10030-6" @default.
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