## Banach Journal of Mathematical Analysis

### Intrinsic square function characterizations of weak Musielak–Orlicz Hardy spaces

Xianjie Yan

#### Abstract

Let $\varphi :\mathbb{R}^{n}\times [0,\infty )\to [0,\infty )$ satisfy that, for any given $x\in \mathbb{R}^{n}$, $\varphi (x,\cdot )$ is an Orlicz function and $\varphi (\cdot ,t)$ is a Muckenhoupt $A_{\infty}(\mathbb{R}^{n})$ weight uniformly in $t\in (0,\infty )$. In this article, via using the atomic and Littlewood–Paley function characterizations of the weak Musielak–Orlicz Hardy space $\mathit{WH}^{\varphi }(\mathbb{R}^{n})$, for any $\alpha \in (0,1]$ and $s\in\mathbb{Z}_{+}$, we first establish its $s$-order intrinsic square function characterizations in terms of the intrinsic Lusin area function $S_{\alpha ,s}$, the intrinsic $g$-function $g_{\alpha ,s}$ and the intrinsic $g_{\lambda }^{*}$-function $g_{\lambda ,\alpha ,s}^{*}$ with the best known range $\lambda \in (2+2(\alpha +s)/n,\infty )$.

#### Article information

Source
Banach J. Math. Anal., Volume 13, Number 4 (2019), 969-988.

Dates
Accepted: 12 February 2019
First available in Project Euclid: 9 October 2019

https://projecteuclid.org/euclid.bjma/1570608170

Digital Object Identifier
doi:10.1215/17358787-2019-0007

Mathematical Reviews number (MathSciNet)
MR4016905

Zentralblatt MATH identifier
07118770

#### Citation

Yan, Xianjie. Intrinsic square function characterizations of weak Musielak–Orlicz Hardy spaces. Banach J. Math. Anal. 13 (2019), no. 4, 969--988. doi:10.1215/17358787-2019-0007. https://projecteuclid.org/euclid.bjma/1570608170

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