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arXiv · 2007.14211

Maximal Function Characterizations of Hardy Spaces on ${\mathbb{R}}^{n}$ with Pointwise Variable Anisotropy

Aiting Wang·Wenhua Wang·Xinping Wang·Baode Li
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Abstract

In 2011, Dekel et al. developed highly geometric Hardy spaces $H^p(\Theta)$, for the full range $0<p\leq 1$, which are constructed by continuous multi-level ellipsoid covers $\Theta$ of $\mathbb{R}^n$ with high anisotropy in the sense that the ellipsoids can change shape rapidly from point to point and from level to level. In this article, if the cover $\Theta$ is pointwise continuous, then the authors further obtain some real-variable characterizations of $H^p(\Theta)$ in terms of the radial, the non-tangential and the tangential maximal functions, which generalize the known results on the anisotropic Hardy spaces of Bownik.

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Aiting Wang, Wenhua Wang, Xinping Wang, Baode Li. 2020-07-28. Maximal Function Characterizations of Hardy Spaces on ${\mathbb{R}}^{n}$ with Pointwise Variable Anisotropy. https://arxiv.org/abs/2007.14211

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