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Intrinsic square function characterizations of variable weak Hardy spaces. (English) Zbl 1434.42032

Summary: 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.

MSC:

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