Why the Riesz transforms are averages of the dyadic shifts?
Petermichl, Stefanie (Institute for Advanced Studies (Princeton, Estats Units d'Amèrica))
Treil, S. (Brown University. Department of Mathematics)
Volberg, Alexander (Michigan State University. Department of Mathematics)

Date:	2002
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.
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Language:	Anglès
Document:	Article ; recerca ; Versió publicada
Subject:	Riesz transforms ; Haar functions ; Dyadic shift ; Dyadic lattice ; Rectifiable measures ; Menger's curvature
Published in:	Publicacions matemàtiques, Vol. Extra (2002) , p. 209-228, ISSN 2014-4350

Adreça alternativa: https://raco.cat/index.php/PublicacionsMatematiques/article/view/38038
DOI: 10.5565/PUBLMAT_Esco02_10

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