TY - JOUR
T1 - The Hörmander multiplier theorem for n-linear operators
AU - Lee, Jongho
AU - Heo, Yaryong
AU - Hong, Sunggeum
AU - Lee, Jin Bong
AU - Park, Bae Jun
AU - Park, Yejune
AU - Yang, Chan Woo
N1 - Funding Information:
Some parts of the results in this paper were obtained during Jongho Lee’s Ph.D. studies at Korea University and will be a part of his thesis.
Funding Information:
This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology NRF-2018R1D1A1B07042871, NRF-2017R1A2B4002316, NRF-2016R1D1A1B01014575, and NRF-2019R1F1A1044075. B. Park is supported in part by a KIAS Individual Grant MG070001 at the Korea Institute for Advanced Study.
Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2021/10
Y1 - 2021/10
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85103147808&partnerID=8YFLogxK
U2 - 10.1007/s00208-021-02162-1
DO - 10.1007/s00208-021-02162-1
M3 - Article
AN - SCOPUS:85103147808
SN - 0025-5831
VL - 381
SP - 499
EP - 555
JO - Mathematische Annalen
JF - Mathematische Annalen
IS - 1-2
ER -