The Hörmander multiplier theorem for n-linear operators

Jongho Lee, Yaryong Heo, Sunggeum Hong, Jin Bong Lee, Bae Jun Park, Yejune Park, Chan Woo Yang

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)499-555
Number of pages57
JournalMathematische Annalen
Volume381
Issue number1-2
DOIs
Publication statusPublished - 2021 Oct

Bibliographical note

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.

ASJC Scopus subject areas

  • General Mathematics

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