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Weak type estimates for cone multipliers on $H^p$ spaces, $p < 1$

Author: Sunggeum Hong
Journal: Proc. Amer. Math. Soc. 128 (2000), 3529-3539
MSC (2000): Primary 42B15, 42B30
Published electronically: May 11, 2000
MathSciNet review: 1690992
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Abstract: We consider operators $T^{\delta}$ associated with the Fourier multipliers \begin{equation*}{\bigg (}1- \frac{\vert{\xi}'\vert^{2}}{{\xi}_{n+1}^{2}} {\bigg... ...d\quad ({\xi}',\xi_{n+1}) \in {\mathbb R}^{n} \times {\mathbb R},\end{equation*} and show that $T^{\delta}$ is of weak type $(p,p)$ on $H^{p}({\mathbb R}^{n+1})$, $0 < p < 1$, for the critical value $\delta = n(\frac{1}{p}-\frac{1}{2}) - \frac{1}{2}$.

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Additional Information

Sunggeum Hong
Affiliation: Department of Mathematics, University of Wisconsin-Madison, Madison, Wisconsin 53706
Address at time of publication: Department of Mathematics, Seoul National University, Seoul, 151-742, Korea

Keywords: Cone multipliers, atomic decomposition of $H^{p}$ spaces
Received by editor(s): September 24, 1998
Received by editor(s) in revised form: January 28, 1999
Published electronically: May 11, 2000
Communicated by: Christopher D. Sogge
Article copyright: © Copyright 2000 American Mathematical Society