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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

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


References [Enhancements On Off] (What's this?)

  • [CT] A.-P. Calderón and A. Torchinsky, Parabolic maximal functions associated with a distribution. II, Advances in Math. 24 (1977), no. 2, 101–171. MR 0450888
  • [CD] R. R. Coifman and Björn Dahlberg, Singular integral characterizations of nonisotropic 𝐻^{𝑝} spaces and the F. and M. Riesz theorem, Harmonic analysis in Euclidean spaces (Proc. Sympos. Pure Math., Williams Coll., Williamstown, Mass., 1978) Proc. Sympos. Pure Math., XXXV, Part, Amer. Math. Soc., Providence, R.I., 1979, pp. 231–234. MR 545260
  • [FS] C. Fefferman and E. M. Stein, 𝐻^{𝑝} spaces of several variables, Acta Math. 129 (1972), no. 3-4, 137–193. MR 0447953
  • [TW] Mitchell H. Taibleson and Guido Weiss, The molecular characterization of certain Hardy spaces, Representation theorems for Hardy spaces, Astérisque, vol. 77, Soc. Math. France, Paris, 1980, pp. 67–149. MR 604370

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DOI: https://doi.org/10.1090/S0002-9939-1990-1007515-X
Article copyright: © Copyright 1990 American Mathematical Society