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TRILINEAR FOURIER MULTIPLIERS ON HARDY SPACES

Part of: Nonlinear operators and their properties Harmonic analysis in several variables

Published online by Cambridge University Press:  15 February 2024

Jin Bong Lee  and
Bae Jun Park Open the ORCID record for Bae Jun Park [Opens in a new window]
Jin Bong Lee
Affiliation:
Research Institute of Mathematics, Seoul National University, Seoul 08826, Republic of Korea ([email protected])
Bae Jun Park*
Affiliation:
Department of Mathematics, Sungkyunkwan University, Suwon 16419, Republic of Korea
*
[email protected]
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Abstract

In this paper, we obtain the $H^{p_1}\times H^{p_2}\times H^{p_3}\to H^p$ boundedness for trilinear Fourier multiplier operators, which is a trilinear analogue of the multiplier theorem of Calderón and Torchinsky [4]. Our result improves the trilinear estimate in [22] by additionally assuming an appropriate vanishing moment condition, which is natural in the boundedness into the Hardy space $H^p$ for $0<p\le 1$.

Keywords

Fourier muitipliersMultilinear operatorsHardy spaces

MSC classification

Primary: 42B15: Multipliers 42B30: $H^p$-spaces 42B25: Maximal functions, Littlewood-Paley theory 47H60: Multilinear and polynomial operators
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 23 , Issue 5 , September 2024 , pp. 2217 - 2278
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Copyright
© The Author(s), 2024. Published by Cambridge University Press

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