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The Hörmander multiplier theorem for n -linear operators
Mathematische Annalen ( IF 1.3 ) Pub Date : 2021-03-25 , DOI: 10.1007/s00208-021-02162-1
Jongho Lee , Yaryong Heo , Sunggeum Hong , Jin Bong Lee , Bae Jun Park , Yejune Park , Chan Woo Yang

In this paper, we study the Hörmander multiplier theorem for multilinear operators. We generalize the result of Tomita (J Funct Anal 259(8):2028–2044, 2010) to wider target spaces and extend that of Grafakos and Van Nguyen (Monatsh Math 190(4):735–753, 2019) to multilinear operators. We indeed give two different proofs: The first proof is based on the results of Grafakos et al. (Can J Math 65(2):299–330, 2013; II J Math Soc Jpn 69(2):529–562, 2017), Grafakos and Van Nguyen (Colloq Math 144(1):1–30, 2016; Monatsh Math 190(4):735–753, 2019), Miyachi and Tomita (Rev Mat Iberoam 29(2):495–530, 2013) and for the second one we provide a new and original approach, inspired by Muscalu et al. (Acta Math 193(2):269–296, 2004). We also give an application and discuss the sharpness of the result.



中文翻译:

n线性算子的Hörmander乘子定理

在本文中,我们研究了多线性算子的Hörmander乘子定理。我们将Tomita(J Funct Anal 259(8):2028-2044,2010)的结果推广到更广泛的目标空间,并将Grafakos和Van Nguyen(Monatsh Math 190(4):735-753,2019)的结果推广到多线性算子。我们确实提供了两种不同的证明:第一种证明是基于Grafakos等人的结果。(Can J Math 65(2):299-330,2013; II J Math Soc Jpn 69(2):529-562,2017),Grafakos和Van Nguyen(Colloq Math 144(1):1-30,2016; Monatsh Math 190(4):735-753,2019),Miyachi和Tomita(Rev Mat Iberoam 29(2):495-530,2013),第二个方法是受Muscalu等人的启发,提供了一种全新的原始方法。(Acta Math 193(2):269-296,2004)。我们还将给出一个应用程序并讨论结果的清晰度。

更新日期:2021-03-25
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