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arXiv · 1703.00228

Conservation de certaines propri\'et\'es \`a travers un contr\^ole \'epars d'un op\'erateur et applications au projecteur de Leray-Hopf

Cristina Benea·Frédéric Bernicot
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Abstract

Nous poursuivons l'\'etude d'un contr\^ole \'epars d'un op\'erateur singulier. Plus pr\'ecis\'ement nous expliquons comment on peut conserver certaines propri\'et\'es de l'op\'erateur initial \`a travers un tel contr\^ole et d\'ecrivons quelques applications: bornitude de l'adjoint de la transform\'ee de Riesz et du projecteur de Leray. De plus, nous nous int\'eresserons \`a donner un regard nouveau sur les dominations \'eparses \`a travers les oscillations et les fonctions carr\'ees localis\'ees. Aussi, nous d\'evoilerons une connexion entre les bons intervalles de la d\'ecomposition \'eparse et une d\'ecomposition 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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Cristina Benea, Frédéric Bernicot. 2017-03-01. Conservation de certaines propri\'et\'es \`a travers un contr\^ole \'epars d'un op\'erateur et applications au projecteur de Leray-Hopf. https://arxiv.org/abs/1703.00228

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