On the $L^p$ boundedness of the non-centered Gaussian Hardy-Littlewood maximal function
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- by Liliana Forzani, Roberto Scotto, Peter Sjögren and Wilfredo Urbina PDF
- Proc. Amer. Math. Soc. 130 (2002), 73-79 Request permission
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 $d\gamma =e^{-|x|^2} dx$.References
- Benjamin Muckenhoupt, Poisson integrals for Hermite and Laguerre expansions, Trans. Amer. Math. Soc. 139 (1969), 231–242. MR 249917, DOI 10.1090/S0002-9947-1969-0249917-9
- Peter Sjögren, A remark on the maximal function for measures in $\textbf {R}^{n}$, Amer. J. Math. 105 (1983), no. 5, 1231–1233. MR 714775, DOI 10.2307/2374340
- Sjögren, P. and Soria, F., Sharp estimates for the noncentered maximal operator associated to Gaussian and other radial measures. Preprint.
- Ana M. Vargas, On the maximal function for rotation invariant measures in $\textbf {R}^n$, Studia Math. 110 (1994), no. 1, 9–17. MR 1279371, DOI 10.4064/sm-110-1-9-17
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
- 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
- © Copyright 2001 American Mathematical Society
- 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
- MathSciNet review: 1855622