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

Author(s): Liliana Forzani; Roberto Scotto; Peter Sjögren; Wilfredo Urbina
Journal: Proc. Amer. Math. Soc. 130 (2002), 73-79.
MSC (1991): Primary 42B25; Secondary 58C05, 60H99
Posted: May 3, 2001
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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:

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: 10.1090/S0002-9939-01-06156-1
PII: S 0002-9939(01)06156-1
Keywords: Fourier analysis, Gaussian measure, maximal function
Received by editor(s): May 15, 2000
Posted: May 3, 2001
Additional Notes: The fourth author was partially supported by CONICIT grant \#6970068
Communicated by: David Preiss
Copyright of article: Copyright 2001, American Mathematical Society

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