On Riesz transforms and maximal functions in the context of Gaussian Harmonic Analysis
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- by H. Aimar, L. Forzani and R. Scotto PDF
- Trans. Amer. Math. Soc. 359 (2007), 2137-2154 Request permission
Abstract:
The purpose of this paper is twofold. We introduce a general maximal function on the Gaussian setting which dominates the Ornstein-Uhlenbeck maximal operator and prove its weak type $(1,1)$ by using a covering lemma which is halfway between Besicovitch and Wiener. On the other hand, by taking as a starting point the generalized Cauchy-Riemann equations, we introduce a new class of Gaussian Riesz Transforms. We prove, using the maximal function defined in the first part of the paper, that unlike the ones already studied, these new Riesz Transforms are weak type $(1,1)$ independently of their orders.References
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Additional Information
- H. Aimar
- Affiliation: Departamento de Matemáticas, Universidad Nacional del Litoral–CONICET, Santa Fe 3000, Argentina
- Email: haimar@ceride.gov.ar
- L. Forzani
- Affiliation: Departamento de Matemáticas, Universidad Nacional del Litoral–CONICET, Santa Fe 3000, Argentina – and – School of Statistics, University of Minnesota, Minneapolis, Minnesota 55455
- Email: lforzani@math.unl.edu.ar
- R. Scotto
- Affiliation: Departamento de Matemáticas, Universidad Nacional del Litoral, Santa Fe 3000, Argentina
- Email: scotto@math.unl.edu.ar
- Received by editor(s): May 5, 2004
- Received by editor(s) in revised form: March 4, 2005
- Published electronically: December 15, 2006
- © Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 359 (2007), 2137-2154
- MSC (2000): Primary 42B20, 42B25; Secondary 42C10, 47D06, 42A50, 60H07
- DOI: https://doi.org/10.1090/S0002-9947-06-04100-6
- MathSciNet review: 2276615