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February, 2019 Parametrized Multilinear Littlewood-Paley Operators on Hardy Spaces
Sha He, Qingying Xue
Taiwanese J. Math. 23(1): 87-101 (February, 2019). DOI: 10.11650/tjm/180507

Abstract

In this paper, we study the parametrized multilinear Marcinkiewicz integral $\mu^{\rho}$ and the multilinear Littlewood-Paley $g_{\lambda}^{*}$-function. We proved that if the kernel $\Omega$ associated to parametrized multilinear Marcinkiewicz integral $\mu^{\rho}$ is homogeneous of degree zero and satisfies the Lipschitz continuous condition, or the kernel $K$ associated to the multilinear Littlewood-Paley $g_{\lambda}^{*}$-function satisfies the Hörmander condition, then they are bounded from $H^{p_1} \times \cdots \times H^{p_m}$ to $L^p$ with $mn/(mn+\gamma) \lt p_1, \ldots, p_m \leq 1$ and $1/p = 1/p_1 + \cdots + 1/p_m$.

Citation

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Sha He. Qingying Xue. "Parametrized Multilinear Littlewood-Paley Operators on Hardy Spaces." Taiwanese J. Math. 23 (1) 87 - 101, February, 2019. https://doi.org/10.11650/tjm/180507

Information

Received: 10 July 2017; Revised: 17 May 2018; Accepted: 20 May 2018; Published: February, 2019
First available in Project Euclid: 9 June 2018

zbMATH: 07021719
MathSciNet: MR3909991
Digital Object Identifier: 10.11650/tjm/180507

Subjects:
Primary: 42B20, 42B25, 42B30

Rights: Copyright © 2019 The Mathematical Society of the Republic of China

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Vol.23 • No. 1 • February, 2019
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