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On the characterization of $ H\sp p({\bf R}\sp n)$ in terms of Fourier multipliers

Author: Akihito Uchiyama
Journal: Proc. Amer. Math. Soc. 109 (1990), 117-123
MSC: Primary 42B30
MathSciNet review: 1007515
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Abstract: Let $ p \in (0,1]$, let $ f \in {L^2}({R^n}) \cap {H^p}({R^n})$ and let $ \theta \in C({R^n}\backslash \left\{ 0 \right\})$ be homogeneous of degree zero. We will give one sufficient condition in order for $ f$ and $ \theta $ to satisfy

$\displaystyle \vert\vert f\vert{\vert _{{H^p}}} \leq C\left\{ {\vert\vert f\ver... ...ft\{ {\theta (\xi )\mathcal{F}f(\xi )} \right\}\vert{\vert _{{L^p}}}} \right\}.$

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Article copyright: © Copyright 1990 American Mathematical Society