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A Multiplier Theorem on Anisotropic Hardy Spaces

Published online by Cambridge University Press:  20 November 2018

Li-an Daniel Wang
Li-an Daniel Wang*
Affiliation:
Department of Mathematics and Statistics, Sam Houston State University, Huntsville, TX, e-mail: ldw021@shsu.edu
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Abstract

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We present a multiplier theorem on anisotropic Hardy spaces. When $m$ satisfies the anisotropic, pointwise Mihlin condition, we obtain boundedness of the multiplier operator ${{T}_{m}}:H_{A}^{p}({{\mathbb{R}}^{n}})\,\to \,H_{A}^{p}({{\mathbb{R}}^{n}})$, 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

42B30(42B2542B35)anisotropic Hardy spacemultiplierFourier transform
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 61 , Issue 2 , 01 June 2018 , pp. 390 - 404
Copyright
Copyright © Canadian Mathematical Society 2018

References

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