Taiwanese Journal of Mathematics

Parametrized Multilinear Littlewood-Paley Operators on Hardy Spaces

Sha He and Qingying Xue

Full-text: Open access

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 $1/p = 1/p_1 + \cdots + 1/p_m$.

Article information

Source
Taiwanese J. Math., Volume 23, Number 1 (2019), 87-101.

Dates
Received: 10 July 2017
Revised: 17 May 2018
Accepted: 20 May 2018
First available in Project Euclid: 9 June 2018

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1528509851

Digital Object Identifier
doi:10.11650/tjm/180507

Mathematical Reviews number (MathSciNet)
MR3909991

Zentralblatt MATH identifier
07021719

Subjects
Primary: 42B20: Singular and oscillatory integrals (Calderón-Zygmund, etc.) 42B25: Maximal functions, Littlewood-Paley theory 42B30: $H^p$-spaces

Keywords
parametrized multilinear Littlewood-Paley $\mu^{\rho}$-function multilinear Littlewood-Paley $g_{\lambda}^*$-function Hardy spaces

Citation

He, Sha; Xue, Qingying. Parametrized Multilinear Littlewood-Paley Operators on Hardy Spaces. Taiwanese J. Math. 23 (2019), no. 1, 87--101. doi:10.11650/tjm/180507. https://projecteuclid.org/euclid.twjm/1528509851


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