[Conserving an operator’s properties through sparse domination and applications to the Leray–Hopf projector]
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.
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.
Revised:
Accepted:
Published online:
Mot clés : Opérateurs épars, poids, espaces de Hardy et BMO
Keywords: Sparse operators, weights, Hardy and BMO spaces
Benea, Cristina 1; Bernicot, Frédéric 1
@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{\textquoteright}un op\'erateur et applications au projecteur de {Leray{\textendash}Hopf}}, journal = {Annales de l'Institut Fourier}, pages = {2329--2379}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {68}, number = {6}, year = {2018}, doi = {10.5802/aif.3211}, language = {fr}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.3211/} }
TY - JOUR AU - Benea, Cristina AU - Bernicot, Frédéric TI - Conservation de certaines propriétés à travers un contrôle épars d’un opérateur et applications au projecteur de Leray–Hopf JO - Annales de l'Institut Fourier PY - 2018 SP - 2329 EP - 2379 VL - 68 IS - 6 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.3211/ DO - 10.5802/aif.3211 LA - fr ID - AIF_2018__68_6_2329_0 ER -
%0 Journal Article %A Benea, Cristina %A Bernicot, Frédéric %T Conservation de certaines propriétés à travers un contrôle épars d’un opérateur et applications au projecteur de Leray–Hopf %J Annales de l'Institut Fourier %D 2018 %P 2329-2379 %V 68 %N 6 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.3211/ %R 10.5802/aif.3211 %G fr %F 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, Volume 68 (2018) no. 6, pp. 2329-2379. doi : 10.5802/aif.3211. https://aif.centre-mersenne.org/articles/10.5802/aif.3211/
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