Why the Riesz transforms are averages of the dyadic shifts?

• Autores: Stefanie Petermichl , Sergei Treil, Alexander Volberg
• Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 46, Nº Extra 1, 2002, págs. 209-228
• Idioma: inglés
• DOI: 10.5565/publmat_esco02_10
• Títulos paralelos:
  • ¿Por qué las transformadas de Riesz son las medias de los desplazamientos diádicos?
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• Resumen

  • The first author showed in [18] that the Hilbert transform lies in the closed convex hull of dyadic singular operators - so called dyadic shifts. We show here that the same is true in any Rn - the Riesz transforms can be obtained as the results of averaging of dyadic shifts. The goal of this paper is almost entirely methodological: we simplify the previous approach, rather than presenting the new one.

    [Proceedings of the 6th International Conference on Harmonic Analysis and Partial Differential Equations, El Escorial (Madrid), 2002].