Tao T., Vargas A.'s A bilinear approach to cone multipliers I PDF

By Tao T., Vargas A.

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Bo1] J. Bourgain, Besicovitch-type maximal operators and applications to Fourier analysis, GAFA 1 (1991), 147–187. [Bo2] J. Bourgain, On the restriction and multiplier problem in R3 , Springer Lecture Notes in Mathematics 1469 (1991), 179–191. [Bo3] J. Bourgain, A remark on Schrodinger operators, Israel J. Math. 77 (1992), 1–16. [Bo4] J. Bourgain, Estimates for cone multipliers, Operator Theory: Advances and Applications 77 (1995), 41–60. [Bo5] J. M. Stein, Princeton University Press (1995), 83–112.

214 T. TAO AND A. VARGAS GAFA ments become inferior to those given by the usual Strichartz’ estimate and H¨ older’s inequality. 10 Acknowledgements The first author was partially supported by NSF grant DMS-9706764. The second author was partially supported by the Spanish DGICYT (grant number PB97-0030) and the European Comission via the TMR network (Harmonic Analysis). The authors thank the reviewer for many helpful comments. References [B] B. Barcelo, On the restriction of the Fourier transform to a conical surface, Trans.

MVV1] A. Moyua, A. Vargas, L. Vega, Schr¨odinger Maximal Function and Restriction Properties of the Fourier transform, International Math. Research Notices 16 (1996). Vol. 10, 2000 BILINEAR CONE MULTIPLIERS I 215 [MVV2] A. Moyua, A. Vargas, L. Vega, Restriction theorems and Maximal operators related to oscillatory integrals in R3 , Duke Math. , to appear. [S] M. Spivak, A Comprehensive Introduction to Differential Geometry, Vol. , 1979. Second Edition. M. Stein, Harmonic Analysis, Princeton University Press, 1993.

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