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Dimension free estimates for the oscillation of riesz transforms

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Abstract

In this paper we establish dimension freeL p(ℝn,|x|α) norm inequalities (1<p<∞) for the oscillation and variation of the Riesz transforms in ℝn. In doing so we findA p -weighted norm inequalities for the oscillation and the variation of the Hilbert transform in ℝ. Some weighted transference results are also proved.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Edinburgh James Clerk Maxwell Building, Edinburgh EH9 3JZ, Scotland, U.K.

    T. A. Gillespie

  2. Departamento de Matemáticas, Facultad de Ciencias, Universidad Autónoma de Madrid, Ciudad Universitaria de Canto Blanco, 28049, Madrid, Spain

    José L. Torrea

Authors
  1. T. A. Gillespie
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  2. José L. Torrea
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Correspondence to T. A. Gillespie.

Additional information

Partially supported by European Commission via the TMR network “Harmonic Analysis”.

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Gillespie, T.A., Torrea, J.L. Dimension free estimates for the oscillation of riesz transforms. Isr. J. Math. 141, 125–144 (2004). https://doi.org/10.1007/BF02772215

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  • DOI: https://doi.org/10.1007/BF02772215

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