Abstract
We give a necessary and sufficient condition for an integrable compactly supported function with mean value zero on the line to be in the Hardy space $H^{1}(\mathbf{R}^{1})$. As a corollary, we obtain a new characterization of $H^{1}(\mathbf{S}^{1})$ and $p$ independence of the spectrum of homogeneous Calderón-Zygmund operators.
Citation
Atanas Stefanov. "Characterizations of $H^{1}$ and applications to singular integrals." Illinois J. Math. 44 (3) 574 - 592, Fall 2000. https://doi.org/10.1215/ijm/1256060417
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