Why the Riesz transforms are averages of the dyadic shifts?
Petermichl, Stefanie ; Treil, Serguei ; Volberg, Alexander L.
Publicacions Matemàtiques, Tome 46 (2002), p. 209-228 / Harvested from Biblioteca Digital de Matemáticas
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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].

Publié le : 2002-01-01
DMLE-ID : 4118 
@article{urn:eudml:doc:41614,
     title = {Why the Riesz transforms are averages of the dyadic shifts?},
     journal = {Publicacions Matem\`atiques},
     volume = {46},
     year = {2002},
     pages = {209-228},
     zbl = {1031.47021},
     mrnumber = {MR1964822},
     language = {en},
     url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41614}
}

Petermichl, Stefanie; Treil, Serguei; Volberg, Alexander L. Why the Riesz transforms are averages of the dyadic shifts?. Publicacions Matemàtiques, Tome 46 (2002) pp. 209-228. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41614/