2 results
A Multiplier Theorem on Anisotropic Hardy Spaces
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- Journal:
- Canadian Mathematical Bulletin / Volume 61 / Issue 2 / 01 June 2018
- Published online by Cambridge University Press:
- 20 November 2018, pp. 390-404
- Print publication:
- 01 June 2018
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- Article
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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.
Anisotropic Hardy-Lorentz Spaces with Variable Exponents
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- Journal:
- Canadian Journal of Mathematics / Volume 69 / Issue 6 / 01 December 2017
- Published online by Cambridge University Press:
- 20 November 2018, pp. 1219-1273
- Print publication:
- 01 December 2017
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In this paper we introduce Hardy-Lorentz spaces with variable exponents associated with dilations in
${{\mathbb{R}}^{n}}$. We establish maximal characterizations and atomic decompositions for our variable
exponent anisotropic Hardy-Lorentz spaces.
