The Hormander multiplier theorem for n-linear operators
- Authors
- Lee, Jongho; Heo, Yaryong; Hong, Sunggeum; Lee, Jin Bong; Park, Bae Jun; Park, Yejune; Yang, Chan Woo
- Issue Date
- 10월-2021
- Publisher
- SPRINGER HEIDELBERG
- Keywords
- 42B25; Primary 42B15; Secondary 42B20
- Citation
- MATHEMATISCHE ANNALEN, v.381, no.1-2, pp.499 - 555
- Indexed
- SCIE
SCOPUS
- Journal Title
- MATHEMATISCHE ANNALEN
- Volume
- 381
- Number
- 1-2
- Start Page
- 499
- End Page
- 555
- URI
- https://scholar.korea.ac.kr/handle/2021.sw.korea/136136
- DOI
- 10.1007/s00208-021-02162-1
- ISSN
- 0025-5831
- Abstract
- In this paper, we study the Hormander 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.
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