| The ρ-variation of the Hermitian Riesz transform |
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| 基金项目： | Supported by Ministerio de Educacian y Ciencia （Spain）, Grants MTM 2008-066621-C02-01/02 and Junta de Andalucfa, Grants FQM-354 and P06-FQM-01509; the first author is supported by Fundacion Carolina, Ministerio de Cultura y Educacion de la Repdblica Argentina and Universidad Nacional del Comahue.Acknowledgements The first author is grateful to Department of Mathematics at Universidad Autonoma de Madrid and Universidad de Malaga for their hospitality during the period of this reserch. |
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| 摘 要： | In this paper we prove the behaviour in weighted Lp spaces of the oscillation and variation of the Hilbert transform and the Riesz transform associated with the Hermite operator of dimension 1. We prove that this operator maps LP（R, w（x）dx） into itself when w is a weight in the Ap class for 1 〈 p 〈 ∞. For p = 1 we get weak type for the A1 class. Weighted estimated are also obtained in the extreme case p = ∞.
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| 关 键 词： | Riesz变换 埃尔米特 变异 希尔伯特变换 加权估计 操作符 证明 p值 |
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