Maximal Function Characterizations of Hardy Spaces on R n with Pointwise Variable Anisotropy

Aiting Wang, Wenhua Wang and Baode Li
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Aiting Wang: College of Mathematics and System Science, Xinjiang University, Urumqi 830017, China
Wenhua Wang: College of Mathematics and System Science, Xinjiang University, Urumqi 830017, China
Baode Li: College of Mathematics and System Science, Xinjiang University, Urumqi 830017, China

Mathematics, 2021, vol. 9, issue 24, 1-19

Abstract: In 2011, Dekel et al. developed highly geometric Hardy spaces H p ( Θ ) , for the full range 0 < p ≤ 1 , which were constructed by continuous multi-level ellipsoid covers Θ of R n 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 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.

Keywords: anisotropy; Hardy space; continuous ellipsoid cover; maximal function (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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