Taiwanese Journal of Mathematics

Intrinsic Square Function Characterizations of Variable Weak Hardy Spaces

Xianjie Yan

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Let $p(\cdot) \colon \mathbb{R}^n \to (0,\infty)$ be a variable exponent function satisfying the globally log-Hölder continuous condition. In this article, via using the atomic and Littlewood-Paley function characterizations of variable weak Hardy space $W\!H^{p(\cdot)}(\mathbb{R}^n)$, the author establishes its intrinsic square function characterizations including the intrinsic Littlewood-Paley $g$-function, the intrinsic Lusin area function and the intrinsic $g_{\lambda}^{\ast}$-function.

Article information

Taiwanese J. Math., Volume 24, Number 1 (2020), 43-62.

Received: 5 September 2018
Accepted: 12 March 2019
First available in Project Euclid: 15 April 2019

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 42B25: Maximal functions, Littlewood-Paley theory
Secondary: 42B30: $H^p$-spaces 42B35: Function spaces arising in harmonic analysis 46E30: Spaces of measurable functions (Lp-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)

Hardy space variable exponent intrinsic square function atomic decomposition


Yan, Xianjie. Intrinsic Square Function Characterizations of Variable Weak Hardy Spaces. Taiwanese J. Math. 24 (2020), no. 1, 43--62. doi:10.11650/tjm/190401. https://projecteuclid.org/euclid.twjm/1555315214

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