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On the $L^p$ boundedness of the non-centered Gaussian Hardy-Littlewood maximal function


Authors: Liliana Forzani, Roberto Scotto, Peter Sjögren and Wilfredo Urbina
Journal: Proc. Amer. Math. Soc. 130 (2002), 73-79
MSC (1991): Primary 42B25; Secondary 58C05, 60H99
DOI: https://doi.org/10.1090/S0002-9939-01-06156-1
Published electronically: May 3, 2001
MathSciNet review: 1855622
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Abstract | References | Similar Articles | Additional Information

Abstract:

The purpose of this paper is to prove the $L^p(\mathcal{R}^n, d\gamma)$ boundedness, for $p>1$, of the non-centered Hardy-Littlewood maximal operator associated with the Gaussian measure $d\gamma=e^{-\vert x\vert^2} dx$.


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

  • 1. Muckenhoupt, B., Poisson integrals for Hermite and Laguerre expansions. Trans. Amer. Math. Soc. 139 (1969), 231-242. MR 40:3158
  • 2. Sjögren, P., A remark on the maximal function for measures in $R^n$. Amer. J. Math. 105 (1983), 1231-1233. MR 86a:28003
  • 3. Sjögren, P. and Soria, F., Sharp estimates for the noncentered maximal operator associated to Gaussian and other radial measures. Preprint.
  • 4. Vargas, A.M., On the maximal function for rotation invariant measures in $R^n $. Studia Math. 110 (1) (1994), 9-17. MR 95e:42019

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Additional Information

Liliana Forzani
Affiliation: Department of Mathematics, Universidad Nacional del Litoral and CONICET, Argentina
Email: forzani@pemas.unl.edu.ar

Roberto Scotto
Affiliation: Department of Mathematics, Universidad Nacional de Salta, Argentina
Email: scotto@math.unl.edu.ar

Peter Sjögren
Affiliation: Department of Mathematics, Göteborg University, SE-412 96 Göteborg, Sweden
Email: peters@math.chalmers.se

Wilfredo Urbina
Affiliation: School of Mathematics, Universidad Central de Venezuela, Caracas 1040, Venezuela
Email: wurbina@euler.ciens.ucv.ve

DOI: https://doi.org/10.1090/S0002-9939-01-06156-1
Keywords: Fourier analysis, Gaussian measure, maximal function
Received by editor(s): May 15, 2000
Published electronically: May 3, 2001
Additional Notes: The fourth author was partially supported by CONICIT grant #6970068
Communicated by: David Preiss
Article copyright: © Copyright 2001 American Mathematical Society

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