Adams inequalities for Riesz subcritical potentials. (March 2020)

• Record Type: Journal Article
• Authors: Fontana, Luigi; Morpurgo, Carlo
• Is Part Of: Nonlinear analysis. Volume 192(2020)
• Publication Date: 2020-03
• Subjects: Adams and Moser–Trudinger inequalities -- Riesz potential; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2019.111662
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We derive Adams inequalities for potentials on general measure spaces, extending and improving previous results in Fontana and Morpurgo (2011). The integral operators involved, which we call "Riesz subcritical", have kernels whose decreasing rearrangements are not worse than that of the Riesz kernel on R n, where the kernel is large, but they behave better where the kernel is small. The new element is a "critical integrability" condition on the kernel at infinity. Typical examples of such kernels are fundamental solutions of nonhomogeneous differential, or pseudo-differential, operators. Another example is the Riesz kernel itself restricted to suitable measurable sets, which we name "Riesz subcritical domains". Such domains are characterized in terms of their growth at infinity. As a consequence of the general results we obtain several new sharp Adams and Moser–Trudinger inequalities on R n, on the hyperbolic space, on Riesz subcritical domains, and on domains where the Poincaré inequality holds.