On the characterization of $H^ p(\textbf {R}^ n)$ in terms of Fourier multipliers
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- by Akihito Uchiyama PDF
- Proc. Amer. Math. Soc. 109 (1990), 117-123 Request permission
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 \[ ||f|{|_{{H^p}}} \leq C\left \{ {||f|{|_{{L^p}}} + ||{\mathcal {F}^{ - 1}}\left \{ {\theta (\xi )\mathcal {F}f(\xi )} \right \}|{|_{{L^p}}}} \right \}.\]References
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Additional Information
- © Copyright 1990 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 109 (1990), 117-123
- MSC: Primary 42B30
- DOI: https://doi.org/10.1090/S0002-9939-1990-1007515-X
- MathSciNet review: 1007515