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

Author(s): Sunggeum Hong
Journal: Proc. Amer. Math. Soc. 128 (2000), 3529-3539.
MSC (2000): Primary 42B15, 42B30
Posted: May 11, 2000
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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 $\delta = n(\frac{1}{p}-\frac{1}{2}) - \frac{1}{2}$.

References:

1.
J. Bourgain, Estimates for the cone multipliers, Opera. Theory Adv. Appl. 77 (1995), 41-60. MR 96m:42022

2.
M. Jodeit Jr., A note on the Fourier multipliers, Proc. Amer. Math. Soc. 27 (1971), 423-424. MR 42:4965

3.
G. Mockenhaupt, A note on the cone multipliers, Proc. Amer. Math. Soc. 117 (1993), 145-152. MR 93c:42015

4.
G. Mockenhaupt, A. Seeger and C. D. Sogge, Wave front sets, local smoothing and Bourgain's circular maximal theorem, Ann. of Math. 136 (1992), 207-218. MR 93i:42009

5.
D. Müller and A. Seeger, Inequalities for spherically symmetric solutions of the wave equation, Math. Z. 3 (1995), 417-426. MR 96e:35093

6.
E. M. Stein, Harmonic analysis : Real variable method, orthogonality and oscillatory integrals, Princeton Univ. Press, 1993. MR 95c:42002

7.
E. M. Stein, M. H. Taibleson and G. Weiss, Weak-type estimates for maximal operators on certain $H^p$ spaces, Rend. Circ. Mat. Palermo(2) suppl. 1 (1981), 81-97. MR 83c:42017

8.
E. M. Stein and G. Weiss, Introduction to Fourier Analysis on Euclidean Spaces, Princeton Univ. Press, 1971. MR 46:4102

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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
Email: hong@math.wisc.edu, shong@math.snu.ac.kr

DOI: 10.1090/S0002-9939-00-05455-1
PII: S 0002-9939(00)05455-1
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
Posted: May 11, 2000
Communicated by: Christopher D. Sogge
Copyright of article: Copyright 2000, American Mathematical Society

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The following works have cited this article

Sunggeum Hong, Some weak type estimates for cone multipliers, Illinois Journal of Mathematics 44, no 3 (2000), 496-515.

Sunggeum Hong, Weak type estimates for cone multipliers on $H^p$ spaces, $p < 1$, Proceedings of the American Mathematical Society 128 (2000), 3529-3539.

Sunggeum Hong, Weak type estimates for cone multipliers on $H^p$ spaces, $p < 1$, Proceedings of the American Mathematical Society 128 (2000), 3529-3539.

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