Banach Journal of Mathematical Analysis

Intrinsic square function characterizations of weak Musielak–Orlicz Hardy spaces

Xianjie Yan

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Let φ:Rn×[0,)[0,) satisfy that, for any given xRn, φ(x,) is an Orlicz function and φ(,t) is a Muckenhoupt A(Rn) weight uniformly in t(0,). In this article, via using the atomic and Littlewood–Paley function characterizations of the weak Musielak–Orlicz Hardy space WHφ(Rn), for any α(0,1] and sZ+, we first establish its s-order intrinsic square function characterizations in terms of the intrinsic Lusin area function Sα,s, the intrinsic g-function gα,s and the intrinsic gλ-function gλ,α,s with the best known range λ(2+2(α+s)/n,).

Article information

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

Received: 2 December 2018
Accepted: 12 February 2019
First available in Project Euclid: 9 October 2019

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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.)

Musielak–Orlicz function weak Musielak–Orlicz Hardy space intrinsic square function atomic decomposition


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.

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