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Fédération Denis Poisson |  |
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Fédération Denis Poisson | |
| HAL : hal-00602760, version 3 |
| arXiv : 1106.4724 |
| Fiche détaillée |  Récupérer au format |
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| Versions disponibles : | v1 (23-06-2011) | v2 (21-10-2011) | v3 (16-01-2012) |
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| A note on $H^p_w$-boundedness of Riesz transforms and $\theta$-Calderón-Zygmund operators through molecular characterization |
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| Luong Dang Ky 1 |
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| (23/06/2011) |
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| Let $0 < p \leq 1$ and $w$ in the Muckenhoupt class $A_1$. Recently, by using the weighted atomic decomposition and molecular characterization; Lee, Lin and Yang \cite{LLY} (J. Math. Anal. Appl. 301 (2005), 394--400) established that the Riesz transforms $R_j, j=1, 2,...,n$, are bounded on $H^p_w(\mathbb R^n)$. In this note we extend this to the general case of weight $w$ in the Muckenhoupt class $A_\infty$ through molecular characterization. One difficulty, which has not been taken care in \cite{LLY}, consists in passing from atoms to all functions in $H^p_w(\mathbb R^n)$. Furthermore, the $H^p_w$-boundedness of $\theta$-Calderón-Zygmund operators are also given through molecular characterization and atomic decomposition. |
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| 1 : | Mathématiques - Analyse, Probabilités, Modélisation - Orléans (MAPMO) |
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Université d'Orléans – CNRS : UMR7349 |
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| Domaine | : | Mathématiques/Analyse classique |
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| Muckenhoupt weights – weighted Hardy spaces – atomic decomposition – molecular characterization – Riesz transforms – Calderón-Zygmund operators |
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| hal-00602760, version 3 | |
| http://hal.archives-ouvertes.fr/hal-00602760 | |
| oai:hal.archives-ouvertes.fr:hal-00602760 | |
| Contributeur : Luong Dang Ky | |
| Soumis le : Samedi 14 Janvier 2012, 00:50:09 | |
| Dernière modification le : Lundi 16 Janvier 2012, 11:17:53 | |
