Duke Mathematical Journal

Improved bounds for Bochner-Riesz and maximal Bochner-Riesz operators

Sanghyuk Lee

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Abstract

In this note we improve the known L p -bounds for Bochner-Riesz operators and their maximal operators.

Article information

Source
Duke Math. J., Volume 122, Number 1 (2004), 205-232.

Dates
First available in Project Euclid: 24 March 2004

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1080137207

Digital Object Identifier
doi:10.1215/S0012-7094-04-12217-1

Mathematical Reviews number (MathSciNet)
MR2046812

Zentralblatt MATH identifier
1072.42009

Subjects
Primary: 42B15 42B25

Citation

Lee, Sanghyuk. Improved bounds for Bochner-Riesz and maximal Bochner-Riesz operators. Duke Math. J. 122 (2004), no. 1, 205--232. doi:10.1215/S0012-7094-04-12217-1. https://projecteuclid.org/euclid.dmj/1080137207


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References

  • J. Bourgain, Besicovitch type maximal operators and applications to Fourier analysis, Geom. Funct. Anal. 1 (1991), 147--187.
  • --. --. --. --., "On the restriction and multiplier problems in $\mathbbR\sp 3$" in Geometric Aspects of Functional Analysis: Israel Seminar (GAFA) 1989/90, Lecture Notes in Math. 1469, Springer, Berlin, 1991, 179--191.
  • A. Carbery, The boundedness of the maximal Bochner-Riesz operator on $L\sp4(R\sp2)$, Duke Math. J. 50 (1983), 409--416.
  • L. Carleson and P. Sjölin, Oscillatory integrals and a multiplier problem for the disc, Studia Math. 44 (1972), 287--299.
  • M. Christ, On almost everywhere convergence of Bochner-Riesz means in higher dimensions, Proc. Amer. Math. Soc. 95 (1985), 16--20.
  • C. Fefferman, Inequalities for strongly singular convolution operators, Acta Math. 124 (1970), 9--36.
  • --. --. --. --., The multiplier problem for the ball, Ann. of Math. (2) 94 (1971), 330--336.
  • S. Lee, Endpoint estimates for the circular maximal function, Proc. Amer. Math. Soc. 131 (2003), 1433--1442.
  • --. --. --. --. Some sharp bounds for the cone multiplier of negative order in $\mathbbR^3$, Bull. London Math. Soc. 35 (2003), 373--390.
  • E. M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Math. Ser. 30, Princeton Univ. Press, Princeton, 1970.
  • --------, Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals, Princeton Math. Ser. 43, Monogr. Harmon. Anal. 3, Princeton Univ. Press, Princeton, 1993.
  • T. Tao, The weak-type endpoint Bochner-Riesz conjecture and related topics, Indiana Univ. Math. J. 47 (1998), 1097--1124.
  • --. --. --. --., The Bochner-Riesz conjecture implies the restriction conjecture, Duke Math. J. 96 (1999), 363--375.
  • --. --. --. --., Endpoint bilinear restriction theorems for the cone, and some sharp null form estimates, Math. Z. 238 (2001), 215--268.
  • --. --. --. --., On the maximal Bochner-Riesz conjecture in the plane for $p<2$, Trans. Amer. Math. Soc. 354 (2002), 1947--1959.
  • --. --. --. --., A Sharp bilinear restriction estimate for paraboloids, Geom. Funct. Anal. 13 (2003), 1359--1384.
  • T. Tao and A. Vargas, A bilinear approach to cone multipliers, I: Restriction estimates, Geom. Funct. Anal. 10 (2000), 185--215.
  • --. --. --. --., A bilinear approach to cone multipliers, II: Application, Geom. Funct. Anal. 10 (2000), 216--258.
  • T. Tao, A. Vargas, and L. Vega, A bilinear approach to the restriction and Kakeya conjectures, J. Amer. Math. Soc. 11 (1998), 967--1000.
  • T. Wolff, An improved bound for Kakeya type maximal functions, Rev. Mat. Iberoamericana 11 (1995), 651--674.
  • --. --. --. --., A mixed norm estimate for the X-ray transform, Rev. Mat. Iberoamericana 14 (1998), 561--600.
  • --. --. --. --., "Recent work connected with the Kakeya problem" in Prospects in Mathematics (Princeton, 1996), Amer. Math. Soc., Providence, 1999, 129--162.
  • --. --. --. --., Local smoothing type estimates on $L\sp p$ for large $p$, Geom. Funct. Anal. 10 (2000), 1237--1288.
  • --. --. --. --., A sharp bilinear cone restriction estimate, Ann. of Math. (2) 153 (2001), 661--698.