Bull. Korean Math. Soc. 2021; 58(2): 365-384
Online first article November 5, 2020 Printed March 31, 2021
https://doi.org/10.4134/BKMS.b200301
Copyright © The Korean Mathematical Society.
Wenhua Wang
Wuhan University
Let $A$ be an expansive dilation on $\mathbb{R}^n$, and $p(\cdot):\mathbb{R}^n\rightarrow(0,\,\infty)$ be a variable exponent function satisfying the globally log-H\"{o}lder continuous condition. Let $H^{p(\cdot)}_A({\mathbb {R}}^n)$ be the variable anisotropic Hardy space defined via the non-tangential grand maximal function. In this paper, the author obtains the boundedness of anisotropic convolutional $\delta$-type Calder\'on-Zygmund operators from $H^{p(\cdot)}_{A}(\mathbb{R}^n)$ to $L^{p(\cdot)}(\mathbb{R}^n)$ or from $H^{p(\cdot)}_{A}(\mathbb{R}^n)$ to itself. In addition, the author also obtains the duality between $H^{p(\cdot)}_ A(\mathbb{R}^n)$ and the anisotropic Campanato spaces with variable exponents.
Keywords: Anisotropy, Hardy space, atom, Calder\'on-Zygmund operator, Campanato space
MSC numbers: Primary 42B20; Secondary 42B30, 46E30
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