An endpoint estimate for the cone multiplier
HTML articles powered by AMS MathViewer
- by Yaryong Heo, Sunggeum Hong and Chan Woo Yang PDF
- Proc. Amer. Math. Soc. 138 (2010), 1333-1347 Request permission
Abstract:
In this paper we consider an endpoint estimate for high-dimensional cone multipliers.References
- Michael Christ and Christopher D. Sogge, On the $L^1$ behavior of eigenfunction expansions and singular integral operators, Miniconferences on harmonic analysis and operator algebras (Canberra, 1987) Proc. Centre Math. Anal. Austral. Nat. Univ., vol. 16, Austral. Nat. Univ., Canberra, 1988, pp. 29–50. MR 953981
- Michael Christ, Weak type $(1,1)$ bounds for rough operators, Ann. of Math. (2) 128 (1988), no. 1, 19–42. MR 951506, DOI 10.2307/1971461
- Gerd Mockenhaupt, A note on the cone multiplier, Proc. Amer. Math. Soc. 117 (1993), no. 1, 145–152. MR 1098404, DOI 10.1090/S0002-9939-1993-1098404-6
- 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).
- J. Bourgain, Estimates for cone multipliers, Geometric aspects of functional analysis (Israel, 1992–1994) Oper. Theory Adv. Appl., vol. 77, Birkhäuser, Basel, 1995, pp. 41–60. MR 1353448
- T. Wolff, Local smoothing type estimates on $L^p$ for large $p$, Geom. Funct. Anal. 10 (2000), no. 5, 1237–1288. MR 1800068, DOI 10.1007/PL00001652
- Izabella Łaba and Thomas Wolff, A local smoothing estimate in higher dimensions, J. Anal. Math. 88 (2002), 149–171. Dedicated to the memory of Tom Wolff. MR 1956533, DOI 10.1007/BF02786576
- Sanghyuk Lee, Improved bounds for Bochner-Riesz and maximal Bochner-Riesz operators, Duke Math. J. 122 (2004), no. 1, 205–232. MR 2046812, DOI 10.1215/S0012-7094-04-12217-1
- Ya Ryong 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, DOI 10.2140/pjm.2001.201.323
- Yaryong Heo, Improved bounds for high dimensional cone multipliers, Indiana Univ. Math. J. 58 (2009), no. 3, 1187–1202. MR 2541363, DOI 10.1512/iumj.2009.58.3553
- Y. Heo, F. Nazarov and A. Seeger, Radial Fourier multipliers in high dimensions, preprint.
- Y. Heo, F. Nazarov and A. Seeger, On radial and conical Fourier multipliers, preprint.
- Elias M. Stein, Harmonic analysis: real-variable methods, orthogonality, and oscillatory integrals, Princeton Mathematical Series, vol. 43, Princeton University Press, Princeton, NJ, 1993. With the assistance of Timothy S. Murphy; Monographs in Harmonic Analysis, III. MR 1232192
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
- 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
- © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 138 (2010), 1333-1347
- MSC (2000): Primary 42B15
- DOI: https://doi.org/10.1090/S0002-9939-09-10112-0
- MathSciNet review: 2578526