Maximal Function Characterizations of Hardy Spaces on Rn with Pointwise Variable Anisotropy

Abstract

In 2011, Dekel et al. developed highly geometric Hardy spaces Hp(Θ), for the full range 0<p≤1, which were constructed by continuous multi-level ellipsoid covers Θ of Rn with high anisotropy in the sense that the ellipsoids can rapidly change shape from point to point and from level to level. In this article, when the ellipsoids in Θ rapidly change shape from level to level, the authors further obtain some real-variable characterizations of Hp(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.