Littlewood-Paley decompositions on manifolds with ends

Jean-Marc Bouclet

Bulletin de la Société Mathématique de France (2010)

  • Volume: 138, Issue: 1, page 1-37
  • ISSN: 0037-9484

Abstract

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For certain non compact Riemannian manifolds with ends which may or may not satisfy the doubling condition on the volume of geodesic balls, we obtain Littlewood-Paley type estimates on (weighted) L p spaces, using the usual square function defined by a dyadic partition.

How to cite

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Bouclet, Jean-Marc. "Littlewood-Paley decompositions on manifolds with ends." Bulletin de la Société Mathématique de France 138.1 (2010): 1-37. <http://eudml.org/doc/272500>.

@article{Bouclet2010,
abstract = {For certain non compact Riemannian manifolds with ends which may or may not satisfy the doubling condition on the volume of geodesic balls, we obtain Littlewood-Paley type estimates on (weighted) $ L^p $ spaces, using the usual square function defined by a dyadic partition.},
author = {Bouclet, Jean-Marc},
journal = {Bulletin de la Société Mathématique de France},
keywords = {Littlewood-Paley decomposition; square function; manifolds with ends; semiclassical analysis},
language = {eng},
number = {1},
pages = {1-37},
publisher = {Société mathématique de France},
title = {Littlewood-Paley decompositions on manifolds with ends},
url = {http://eudml.org/doc/272500},
volume = {138},
year = {2010},
}

TY - JOUR
AU - Bouclet, Jean-Marc
TI - Littlewood-Paley decompositions on manifolds with ends
JO - Bulletin de la Société Mathématique de France
PY - 2010
PB - Société mathématique de France
VL - 138
IS - 1
SP - 1
EP - 37
AB - For certain non compact Riemannian manifolds with ends which may or may not satisfy the doubling condition on the volume of geodesic balls, we obtain Littlewood-Paley type estimates on (weighted) $ L^p $ spaces, using the usual square function defined by a dyadic partition.
LA - eng
KW - Littlewood-Paley decomposition; square function; manifolds with ends; semiclassical analysis
UR - http://eudml.org/doc/272500
ER -

References

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  1. [1] J.-M. Bouclet – « Semi-classical functional calculus on manifolds with ends and weighted L p estimates », to appear in Ann. Inst. Fourier. Zbl1236.58033MR2918727
  2. [2] —, « Strichartz estimates on asymptotically hyperbolic manifolds », to appear in Analysis & PDE. Zbl1230.35027
  3. [3] J.-M. Bouclet & N. Tzvetkov – « Strichartz estimates for long range perturbations », Amer. J. Math.129 (2007), p. 1565–1609. Zbl1154.35077MR2369889
  4. [4] —, « On global Strichartz estimates for non-trapping metrics », J. Funct. Anal.254 (2008), p. 1661–1682. Zbl1168.35005MR2396017
  5. [5] N. Burq, P. Gérard & N. Tzvetkov – « Strichartz inequalities and the nonlinear Schrödinger equation on compact manifolds », Amer. J. Math.126 (2004), p. 569–605. Zbl1067.58027MR2058384
  6. [6] T. Coulhon, X. T. Duong & X. D. Li – « Littlewood-Paley-Stein functions on complete Riemannian manifolds for 1 ≤ p ≤ 2 », Studia Math.154 (2003), p. 37–57. Zbl1035.42014MR1949048
  7. [7] S. Klainerman & I. Rodnianski – « A geometric approach to the Littlewood-Paley theory », Geom. Funct. Anal.16 (2006), p. 126–163. Zbl1206.35080MR2221254
  8. [8] N. Lohoué – « Estimation des fonctions de Littlewood-Paley-Stein sur les variétés riemanniennes à courbure non positive », Ann. Sci. École Norm. Sup.20 (1987), p. 505–544. Zbl0636.43002MR932796
  9. [9] G. Olafsson & S. Zheng – « Harmonic analysis related to Schrödinger operators », in Radon transforms, geometry, and wavelets, Contemp. Math., vol. 464, Amer. Math. Soc., 2008, p. 213–230. Zbl1256.42031MR2440138
  10. [10] W. Schlag – « A remark on Littlewood-Paley theory for the distorted Fourier transform », Proc. Amer. Math. Soc. 135 (2007), p. 437–451 (electronic). Zbl1159.42008MR2255290
  11. [11] —, « Lecture notes on harmonic analysis », http://www.math.uchicago.edu/~schlag/book.pdf. Zbl0991.42010
  12. [12] C. D. Sogge – Fourier integrals in classical analysis, Cambridge Tracts in Mathematics, vol. 105, Cambridge Univ. Press, 1993. Zbl0783.35001MR1205579
  13. [13] E. M. Stein – Singular integrals and differentiability properties of functions, Princeton Mathematical Series, No. 30, Princeton Univ. Press, 1970. Zbl0207.13501MR290095
  14. [14] M. E. Taylor – « L p -estimates on functions of the Laplace operator », Duke Math. J.58 (1989), p. 773–793. Zbl0691.58043MR1016445
  15. [15] —, Partial differential equations. III, Applied Mathematical Sciences, vol. 117, Springer, 1997. Zbl1206.35004

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