Why the Riesz transforms are averages of the dyadic shifts?

Stefanie Petermichl; Serguei Treil; Alexander L. Volberg

Publicacions Matemàtiques (2002)

  • Volume: 46, Issue: Extra, page 209-228
  • ISSN: 0214-1493

Abstract

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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].

How to cite

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Petermichl, Stefanie, Treil, Serguei, and Volberg, Alexander L.. "Why the Riesz transforms are averages of the dyadic shifts?." Publicacions Matemàtiques 46.Extra (2002): 209-228. <http://eudml.org/doc/41614>.

@article{Petermichl2002,
abstract = {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].},
author = {Petermichl, Stefanie, Treil, Serguei, Volberg, Alexander L.},
journal = {Publicacions Matemàtiques},
keywords = {Riesz transforms; Haar functions; dyadic shift; dyadic lattice; rectifiable measures; Menger's curvature; averaging},
language = {eng},
number = {Extra},
pages = {209-228},
title = {Why the Riesz transforms are averages of the dyadic shifts?},
url = {http://eudml.org/doc/41614},
volume = {46},
year = {2002},
}

TY - JOUR
AU - Petermichl, Stefanie
AU - Treil, Serguei
AU - Volberg, Alexander L.
TI - Why the Riesz transforms are averages of the dyadic shifts?
JO - Publicacions Matemàtiques
PY - 2002
VL - 46
IS - Extra
SP - 209
EP - 228
AB - 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].
LA - eng
KW - Riesz transforms; Haar functions; dyadic shift; dyadic lattice; rectifiable measures; Menger's curvature; averaging
UR - http://eudml.org/doc/41614
ER -

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