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

In 2011, Dekel et al. developed highly geometric Hardy spaces $H^p(Θ)$, for the full range $0<p\leq 1$, which are constructed by continuous multi-level ellipsoid covers $Θ$ 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 $Θ$ is pointwise continuous, then the authors further obtain some real-variable characterizations of $H^p(Θ)$ 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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