Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Some convolution inequalities and their applications


Author: Daniel M. Oberlin
Journal: Trans. Amer. Math. Soc. 354 (2002), 2541-2556
MSC (2000): Primary 42B10
DOI: https://doi.org/10.1090/S0002-9947-01-02921-X
Published electronically: November 30, 2001
MathSciNet review: 1885663
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We introduce a class of convolution inequalities and study the implications of these inequalities for certain problems in harmonic analysis.


References [Enhancements On Off] (What's this?)

  • 1. J.-G. Bak, An $L^{p}$-$L^{q}$ estimate for Radon transforms associated to polynomials, Duke Math. J. 101 (2000), 259-269. MR 2001b:42012
  • 2. J.-G. Bak, D.M. Oberlin, and A. Seeger, Two endpoint bounds for generalized Radon transforms in the plane, Revista Math. (to appear).
  • 3. B. B. Taberner, On the restriction of the Fourier transform to a conical surface, Trans. Amer. Math. Soc. 292 (1985), 321-333. MR 86k:42023
  • 4. M. Christ, Estimates for the $k-$plane transform, Indiana Univ. Math. J. 33 (1984), 891-910. MR 86k:44004
  • 5. -, On the restriction of the Fourier transform to curves: endpoint results and the degenerate case, Trans. Amer. Math. Soc. 287 (1985), 223-238. MR 87b:42018
  • 6. S.W. Drury, Restrictions of Fourier transforms to curves, Ann. Inst. Fourier, Grenoble 35 (1985), 117-123. MR 86e:42026
  • 7. -, A survey of $k-$plane transforms, Contemp. Math. 91 (1989), 43-55. MR 92b:44002
  • 8. -, Degenerate curves and harmonic analysis, Math. Proc. Camb. Phil. Soc. 108 (1990), 89-96. MR 91h:42021
  • 9. S.W. Drury and K. Guo, Convolution estimates related to surfaces of half the ambient dimension, Math. Proc. Camb. Phil. Soc. 110 (1991), 151-159. MR 92j:42012
  • 10. -, Some remarks on the restriction of the Fourier transform to surfaces, Math. Proc. Camb. Phil. Soc. 113 (1993), 153-159. MR 94f:42020
  • 11. S.W. Drury and B.P. Marshall, Fourier restriction theorems for curves with affine and Euclidean arclengths, Math. Proc. Camb. Phil. Soc. 97 (1985), 111-125. MR 87b:42019
  • 12. J. Harmse, On Lebesgue space estimates for the wave equation, Indiana Univ. Math. J. 39 (1990), 229-248. MR 91j:35158
  • 13. G.H. Hardy, J.E. Littlewood, and G. Pólya, Inequalities, Cambridge University Press, 1959. MR 13:727e (1952 ed.)
  • 14. D.M. Oberlin, Convolution estimates for some distributions with singularities on the light cone, Duke Math. J. 59 (1989), 747-757. MR 91f:46053
  • 15. -, Multilinear proofs for two theorems on circular averages, Colloq. Math. 63 (1992), 187-190. MR 93m:42005
  • 16. -, Convolution with affine arclength measures in the plane, Proc. Amer. Math. Soc. 127 (1999), 3591-3592. MR 2000c:42016
  • 17. -, Convolution with measure on hypersurfaces, Math. Proc. Camb. Phil. Soc. 129 (2000), 517-526. MR 2001j:42014
  • 18. -, Convolution with measures on polynomial curves, Math. Scand. (to appear).
  • 19. -, Fourier restriction for affine arclengthmeasures in the plane, Proc. Amer. Math. Soc. 129 (2001), 3303-3305. CMP 2001:16

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 42B10

Retrieve articles in all journals with MSC (2000): 42B10


Additional Information

Daniel M. Oberlin
Affiliation: Department of Mathematics, Florida State University, Tallahassee, Florida 32306-4510
Email: oberlin@math.fsu.edu

DOI: https://doi.org/10.1090/S0002-9947-01-02921-X
Keywords: Convolution, restriction
Received by editor(s): May 2, 2001
Received by editor(s) in revised form: June 21, 2001
Published electronically: November 30, 2001
Additional Notes: The author was partially supported by the NSF
Article copyright: © Copyright 2001 American Mathematical Society

American Mathematical Society