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# A Multiplier Theorem on Anisotropic Hardy Spaces

Published:2017-06-15
Printed: Jun 2018
• Li-an Daniel Wang,
Department of Mathematics and Statistics, Sam Houston State University, Huntsville, TX , USA
 Format: LaTeX MathJax PDF

## Abstract

We present a multiplier theorem on anisotropic Hardy spaces. When $m$ satisfies the anisotropic, pointwise Mihlin condition, we obtain boundedness of the multiplier operator $T_m : H_A^p (\mathbb R^n) \rightarrow H_A^p (\mathbb R^n)$, for the range of $p$ that depends on the eccentricities of the dilation $A$ and the level of regularity of a multiplier symbol $m$. This extends the classical multiplier theorem of Taibleson and Weiss.
 Keywords: anisotropic Hardy space, multiplier, Fourier transform
 MSC Classifications: 42B30 - $H^p$-spaces 42B25 - Maximal functions, Littlewood-Paley theory 42B35 - Function spaces arising in harmonic analysis

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