Conservation de certaines propriétés à travers un contrôle épars d’un opérateur et applications au projecteur de Leray–Hopf

Benea, Cristina; Bernicot, Frédéric

doi:10.5802/aif.3211

Benea, Cristina ; Bernicot, Frédéric

Annales de l'Institut Fourier, Tome 68 (2018) no. 6, pp. 2329-2379.

Résumé
Abstract

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.

Reçu le : 2017-02-26
Révisé le : 2017-07-24
Accepté le : 2017-11-06
Publié le : 2018-11-22

DOI : https://doi.org/10.5802/aif.3211
Classification : 42B15, 42B25, 42B35
Mots clés : Opérateurs épars, poids, espaces de Hardy et BMO

@article{AIF_2018__68_6_2329_0,
     author = {Benea, Cristina and Bernicot, Fr\'ed\'eric},
     title = {Conservation de certaines propri\'et\'es \`a travers un contr\^ole \'epars d'un op\'erateur et applications au projecteur de Leray--Hopf},
     journal = {Annales de l'Institut Fourier},
     pages = {2329--2379},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {68},
     number = {6},
     year = {2018},
     doi = {10.5802/aif.3211},
     language = {fr},
     url = {archive.numdam.org/item/AIF_2018__68_6_2329_0/}
}

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/item/AIF_2018__68_6_2329_0/

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