Geodesic
Essential norm estimates for multilinear singular and fractional integrals
Commentationes Mathematicae, Tome 59 (2019) no. 1-2, p. 81−93.

Voir la notice de l'article provenant de la source Annales Societatis Mathematicae Polonae Series

We derive lower two-weight estimates for the essential norm (measure of noncompactness) for multilinear Hilbert and Riesz transforms, and Riesz potential operators in Banach function lattices. As a corollary we have appropriate results in weighted Lebesgue spaces. From these statements we conclude that there is no \((m+1)\)-tuple of weights \((v,w_1, \dots, w_m)\) for which these operators are compact from \(L^{p_1}_{w_1} \times \dots \times L^{p_m}_{w_m}\) to \(L^q_v\).
DOI : 10.14708/cm.v59i1-2.6523
Classification : 46B70, 42B20, 46E30
Mots-clés : Multilinear Hilbert and Riesz transforms, multilinear fractional integrals, measure of noncompactness, weighted inequalities, Banach function lattices 
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Alexander Meskhi. Essential norm estimates for multilinear singular and fractional integrals. Commentationes Mathematicae, Tome 59 (2019) no. 1-2, p.  81−93. doi : 10.14708/cm.v59i1-2.6523. http://geodesic.mathdoc.fr/articles/10.14708/cm.v59i1-2.6523/

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