Conservation de certaines propriétés à travers un contrôle épars d’un opérateur et applications au projecteur de Leray–Hopf
Annales de l'Institut Fourier, Tome 68 (2018) no. 6, pp. 2329-2379.

Nous poursuivons l’étude d’un contrôle épars d’un opérateur singulier. Plus précisément nous expliquons comment on peut conserver certaines propriétés de l’opérateur initial à travers un tel contrôle et décrivons quelques applications : bornitude de l’adjoint de la transformée de Riesz et du projecteur de Leray. De plus, nous nous intéresserons à donner un regard nouveau sur les dominations éparses à travers les oscillations et les fonctions carrées localisées. Aussi, nous dévoilerons une connexion entre les bons intervalles de la décomposition éparse et une décomposition atomique.

We pursue the study of a sparse control for a singular operator. More precisely, we describe how one can track some properties of the initial operator, through such a control and describe also some applications: boundedness of the adjoint of a Riesz transform and of the Leray projector. Moreover, we will be interested in giving a new insight on the sparse domination through the oscillations and the localized square functions. Also, we will reveal a connection between the good intervals of the sparse domination and the atomic decomposition for a function in a Hardy space.

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DOI : 10.5802/aif.3211
Classification : 42B15, 42B25, 42B35
Mot clés : Opérateurs épars, poids, espaces de Hardy et BMO
Keywords: Sparse operators, weights, Hardy and BMO spaces
Benea, Cristina 1 ; Bernicot, Frédéric 1

1 CNRS - Université de Nantes Laboratoire Jean Leray 44322 Nantes (France)
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Benea, Cristina; Bernicot, Frédéric. Conservation de certaines propriétés à travers un contrôle épars d’un opérateur et applications au projecteur de Leray–Hopf. Annales de l'Institut Fourier, Tome 68 (2018) no. 6, pp. 2329-2379. doi : 10.5802/aif.3211. http://archive.numdam.org/articles/10.5802/aif.3211/

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