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| Paper IPM / M / 17679 |
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| Abstract: | |
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This contribution is based on joint work with Hormozi et al. (J. Fourier Anal. Appl. 29:49, 2023). We simplify and shorten the proofs of the main results of Shi et al. (J. Math. Pures Appl. 101:394�â??413, 2014) significantly. In particular, the new proof for Shi et al. (J. Math. Pures Appl. 101:394�â??413, 2014; Theorem 1.1) is quite short and, unlike the original proof, does not rely on the properties of the �â??Marcinkiewicz function�â?ïÿý. This allows us to get a precise linear dependence on Dini constants with a subsequent application to Littlewood�â??Paley operators by the well-known techniques.
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