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

Benea, Cristina¹ ; Bernicot, Frédéric¹

¹ CNRS - Université de Nantes Laboratoire Jean Leray 44322 Nantes (France)

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

Résumé (VO)

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.

Abstract

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.

Détail

Reçu le : 2017-02-27
Révisé le : 2017-07-25
Accepté le : 2017-11-07
Publié le : 2018-11-23

DOI : 10.5802/aif.3211

Classification : 42B15, 42B25, 42B35
Mots-clés : Opérateurs épars, poids, espaces de Hardy et BMO
Keywords: Sparse operators, weights, Hardy and BMO spaces

Licence : CC-BY-ND 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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