Fourier transform of anisotropic Hardy spaces
Marcin Bownik, Li-An Daniel Wang
TL;DR
This paper extends Fourier transform estimates for Hardy spaces to anisotropic settings, deriving necessary conditions for multipliers and strengthening the Hardy-Littlewood inequality using rearrangement techniques.
Contribution
It introduces anisotropic Hardy space Fourier transform estimates, providing new necessary conditions for multipliers and an improved Hardy-Littlewood inequality.
Findings
Extended Taibleson and Weiss estimate to anisotropic Hardy spaces
Derived necessary conditions for multiplier operators in anisotropic setting
Strengthened Hardy-Littlewood inequality with rearrangement argument
Abstract
We extend an estimate of Taibleson and Weiss, regarding Fourier transform of Hardy spaces, to the aniostropic setting. As consequences, we obtain necessary conditions for multiplier operators, and the anisotropic version of the Hardy-Littlewood inequality. This last inequality is strengthened with a rearrangement argument.
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Taxonomy
TopicsAdvanced Harmonic Analysis Research · Advanced Mathematical Physics Problems · Holomorphic and Operator Theory