Taiwanese Journal of Mathematics


Baode Li, Xingya Fan, and Dachun Yang

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Let $\varphi : \mathbb{R}^n\times [0,\,\infty)\to[0,\infty)$ be a Musielak-Orlicz function and $A$ an expansive dilation. Let $H^\varphi_A({\mathbb {R}}^n)$ be the anisotropic Hardy space of Musielak-Orlicz type defined via the grand maximal function. Its atomic characterization and some other maximal function characterizations of $H^\varphi_A({\mathbb {R}^n})$, in terms of the radial, the non-tangential and the tangential maximal functions, are known. In this article, the authors further obtain their characterizations in terms of the Lusin-area function, the $g$-function or the $g^\ast_\lambda$-function via first establishing an anisotropic Peetre's inequality of Musielak-Orlicz type. Moreover, the range of $\lambda$ in the $g^\ast_\lambda$-function characterization of $H^\varphi_A({\mathbb {R}}^n)$ coincides with the known best conclusions in the case when $H^\varphi_A({\mathbb {R}}^n)$ is the classical Hardy space $H^p({\mathbb{R}}^n)$ or the anisotropic Hardy space $H^p_A({\mathbb {R}}^n)$ or their weighted variants, where $p\in(0,\,1]$.

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Taiwanese J. Math., Volume 19, Number 1 (2015), 279-314.

First available in Project Euclid: 4 July 2017

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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.)

Littlewood-Paley function anisotropic expansive dilation Muckenhoupt weight Musielak-Orlicz function Hardy space


Li, Baode; Fan, Xingya; Yang, Dachun. LITTLEWOOD-PALEY CHARACTERIZATIONS OF ANISOTROPIC HARDY SPACES OF MUSIELAK-ORLICZ TYPE. Taiwanese J. Math. 19 (2015), no. 1, 279--314. doi:10.11650/tjm.19.2015.4692. https://projecteuclid.org/euclid.twjm/1499133630

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