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arXiv · 2211.02991

Sharp Adams inequalities with exact growth conditions on metric measure spaces and applications

Carlo Morpurgo·Liuyu Qin
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Abstract

Adams inequalities with exact growth conditions are derived for Riesz-like potentials on metric measure spaces. The results extend and improve those obtained recently on $\mathbb R^n$ by the second author, for Riesz-like convolution operators. As a consequence, we will obtain new sharp Moser-Trudinger inequalities with exact growth conditions on $\mathbb R^n$, the Heisenberg group, and Hadamard manifolds. On $\mathbb R^n$ such inequalities will be used to prove the existence of radial ground states solutions for a class of quasilinear elliptic equations, extending results due to Masmoudi and Sani.

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Carlo Morpurgo, Liuyu Qin. 2022-11-05. Sharp Adams inequalities with exact growth conditions on metric measure spaces and applications. https://arxiv.org/abs/2211.02991

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