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Search: All articles in the CJM digital archive with keyword maximal function

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1. CJM Online first

Almeida, Víctor; Betancor, Jorge J.; Rodríguez-Mesa, Lourdes
Anisotropic Hardy-Lorentz spaces with variable exponents
In this paper we introduce Hardy-Lorentz spaces with variable exponents associated to dilations in ${\mathbb R}^n$. We establish maximal characterizations and atomic decompositions for our variable exponent anisotropic Hardy-Lorentz spaces.

Keywords:variable exponent Hardy space, Hardy-Lorentz space, anisotropic Hardy space, maximal function, atomic decomposition
Categories:42B30, 42B25, 42B35

2. CJM 2015 (vol 67 pp. 1161)

Zhang, Junqiang; Cao, Jun; Jiang, Renjin; Yang, Dachun
Non-tangential Maximal Function Characterizations of Hardy Spaces Associated with Degenerate Elliptic Operators
Let $w$ be either in the Muckenhoupt class of $A_2(\mathbb{R}^n)$ weights or in the class of $QC(\mathbb{R}^n)$ weights, and $L_w:=-w^{-1}\mathop{\mathrm{div}}(A\nabla)$ the degenerate elliptic operator on the Euclidean space $\mathbb{R}^n$, $n\ge 2$. In this article, the authors establish the non-tangential maximal function characterization of the Hardy space $H_{L_w}^p(\mathbb{R}^n)$ associated with $L_w$ for $p\in (0,1]$ and, when $p\in (\frac{n}{n+1},1]$ and $w\in A_{q_0}(\mathbb{R}^n)$ with $q_0\in[1,\frac{p(n+1)}n)$, the authors prove that the associated Riesz transform $\nabla L_w^{-1/2}$ is bounded from $H_{L_w}^p(\mathbb{R}^n)$ to the weighted classical Hardy space $H_w^p(\mathbb{R}^n)$.

Keywords:degenerate elliptic operator, Hardy space, square function, maximal function, molecule, Riesz transform
Categories:42B30, 42B35, 35J70

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