Adams inequalities with exact growth condition for Riesz-like potentials on $\mathbb{R}^n$

TL;DR

This paper establishes sharp Adams and Moser-Trudinger inequalities with precise growth conditions for Riesz potentials, fractional Laplacians, and general elliptic operators on Euclidean space.

Contribution

It introduces exact growth conditions for Adams and Moser-Trudinger inequalities applicable to Riesz and Riesz-like potentials, extending the scope of these inequalities.

Findings

Sharp Adams inequalities with exact growth conditions for Riesz potentials.

Moser-Trudinger inequalities with precise growth for fractional Laplacians.

Extension to general homogeneous elliptic operators.

Abstract

We derive sharp Adams inequalities with exact growth condition for the Riesz potential as well as more general Riesz-like potentials on R^n. We also obtain Moser-Trudinger inequalities with exact growth condition for the fractional Laplacian, and for general homogeneous elliptic differential operators with constant coefficients.