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 Rn, 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 Rn, on the hyperbolic space, on Riesz subcritical domains, and on domains where the Poincaré inequality holds.

Fontana, L., Morpurgo, C. (2020). Adams inequalities for Riesz subcritical potentials. NONLINEAR ANALYSIS, 192(March 2020) [10.1016/j.na.2019.111662].

Adams inequalities for Riesz subcritical potentials

Fontana, L
;
2020

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 Rn, 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 Rn, on the hyperbolic space, on Riesz subcritical domains, and on domains where the Poincaré inequality holds.
Articolo in rivista - Articolo scientifico
Adams and Moser–Trudinger inequalities; Riesz potential;
English
22-ott-2019
2020
192
March 2020
111662
reserved
Fontana, L., Morpurgo, C. (2020). Adams inequalities for Riesz subcritical potentials. NONLINEAR ANALYSIS, 192(March 2020) [10.1016/j.na.2019.111662].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/272884
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