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An endpoint estimate for the cone multiplier


Authors: Yaryong Heo, Sunggeum Hong and Chan Woo Yang
Journal: Proc. Amer. Math. Soc. 138 (2010), 1333-1347
MSC (2000): Primary 42B15
DOI: https://doi.org/10.1090/S0002-9939-09-10112-0
Published electronically: November 23, 2009
MathSciNet review: 2578526
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Abstract: In this paper we consider an endpoint estimate for high-dimensional cone multipliers.


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  • 1. M. Christ and C. D. Sogge, On the $ L\sp 1$ behavior of eigenfunction expansions and singular integral operators, in Miniconferences on harmonic analysis and operator algebras (Canberra, 1987), 29-50, Austral. Nat. Univ., Canberra, 1988. MR 0953981 (89k:42024)
  • 2. M. Christ, Weak type $ (1,1)$ bounds for rough operators, Ann. of Math. (2) 128 (1988), no. 1, 19-42. MR 0951506 (89m:42013)
  • 3. G. Mockenhaupt, A note on the cone multiplier, Proc. Amer. Math. Soc. 117 (1993), no. 1, 145-152. MR 1098404 (93c:42015)
  • 4. G. Garrigós and A. Seeger, On plate decompositions of cone multipliers, Proceedings of the Conference on Harmonic Analysis and Its Applications, Hokkaido University, Sapporo (2005).
  • 5. J. Bourgain, Estimates for cone multipliers, in Geometric aspects of functional analysis (Israel, 1992-1994), 41-60, Birkhäuser, Basel, 1995. MR 1353448 (96m:42022)
  • 6. T. Wolff, Local smoothing type estimates on $ L\sp p$ for large $ p$, Geom. Funct. Anal. 10 (2000), no. 5, 1237-1288. MR 1800068 (2001k:42030)
  • 7. I. Łaba and T. Wolff, A local smoothing estimate in higher dimensions, J. Anal. Math. 88 (2002), 149-171. MR 1956533 (2005b:35015)
  • 8. S. Lee, Improved bounds for Bochner-Riesz and maximal Bochner-Riesz operators, Duke Math. J. 122 (2004), no. 1, 205-232. MR 2046812 (2005e:42042)
  • 9. Y. R. Heo, An endpoint estimate for some maximal operators associated to submanifolds of low codimension, Pacific J. Math. 201 (2001), no. 2, 323-338. MR 1875897 (2002j:42030)
  • 10. Y. Heo, Improved bounds for high dimensional cone multipliers, Indiana Univ. Math. J. 58 (2009), no. 3, 1187-1202. MR 2541363
  • 11. Y. Heo, F. Nazarov and A. Seeger, Radial Fourier multipliers in high dimensions, preprint.
  • 12. Y. Heo, F. Nazarov and A. Seeger, On radial and conical Fourier multipliers, preprint.
  • 13. E. M. Stein, Harmonic analysis: Real-variable methods, orthogonality, and oscillatory integrals, Princeton Univ. Press, Princeton, NJ, 1993. MR 1232192 (95c:42002)

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Additional Information

Yaryong Heo
Affiliation: Department of Mathematics, University of Wisconsin-Madison, Madison, Wisconsin 53706
Address at time of publication: Pohang Mathematics Institute, Pohang University of Science & Technology, Pohang 790-784, Korea
Email: heo@math.wisc.edu, heo@postech.ac.kr

Sunggeum Hong
Affiliation: Department of Mathematics, Chosun University, Gwangju 501-759, Republic of Korea
Email: skhong@mail.chosun.ac.kr

Chan Woo Yang
Affiliation: Department of Mathematics, Korea University, Seoul 136-701, Republic of Korea
Email: cw_yang@korea.ac.kr

DOI: https://doi.org/10.1090/S0002-9939-09-10112-0
Keywords: Cone multipliers.
Received by editor(s): October 6, 2008
Received by editor(s) in revised form: July 8, 2009
Published electronically: November 23, 2009
Additional Notes: The first author was supported by the Korea Research Foundation Grant funded by the Korean Government (KRF-2008-357-C00002).
The second author was supported by the Korea Research Foundation Grant funded by the Korean Government (MEST) (No. 2009-0065011).
The third author was supported by the Korea Research Foundation Grant funded by the Korean Government (KRF-2008-331-C00016).
Communicated by: Michael T. Lacey
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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