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Journées équations aux dérivées partielles

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Cristina Benea; Camil Muscalu
Mixed-norm estimates for paraproducts
Journées équations aux dérivées partielles (2016), Exp. No. 2, 10 p., doi: 10.5802/jedp.643
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Résumé - Abstract

We present a new approach to the study of singular multi-parameter multilinear Fourier multipliers via multiple vector-valued inequalities. This summarizes some of our results from [1] and [2]. The main example is the bi-parameter paraproduct $\Pi \otimes \Pi $, for which we prove estimates within the whole range of admissible Lebesgue estimates.


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[2] Cristina Benea & Camil Muscalu, “Quasi-Banach Valued Inequalities via the Helicoidal method”, https://arxiv.org/pdf/1609.01090v1.pdf, 2016
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[11] Camil Muscalu, Jill Pipher, Terence Tao & Christoph Thiele, “Bi-parameter paraproducts”, Acta Mathematica (2004), p. 269-296  MR 2134868
[12] Camil Muscalu, Jill Pipher, Terence Tao & Christoph Thiele, “Multi-parameter paraproducts”, Rev. Mat. Iberoamericana (2006), p. 963-976
[13] Camil Muscalu & Wilhem Schlag, Classical and Multilinear Harmonic Analysis, Cambridge University Press, 2013
[14] Camil Muscalu, Terence Tao & Christoph Thiele, “Multi-linear operators given by singular multipliers”, J. Amer. Math. Soc. (2002), p. 469-496
[15] Zhuoping Ruan, “Multi-parameter Hardy spaces via discrete Littlewood-Paley theory”, Anal. Theory Appl. 26 (2010) no. 2, p. 122-139
[16] Prabath Silva, “Vector Valued Inequalities for Families of Bilinear Hilbert Transforms and Applications to Bi-parameter Problems”, J. Lond. Math. Soc. (2014), p. 695-724
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