Why the Riesz transforms are averages of the dyadic shifts?
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...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2002 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:138527 |
| Acceso en línea: | https://ddd.uab.cat/record/138527 https://dx.doi.org/urn:doi:10.5565/PUBLMAT_Esco02_10 |
| Access Level: | acceso abierto |
| Palabra clave: | Riesz transforms Haar functions Dyadic shift Dyadic lattice Rectifiable measures Menger's curvature |
| Sumario: | 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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