Sharp exponential integrability for critical Riesz potentials and fractional Laplacians on R^n

Abstract

We derive sharp Adams inequalities for the Riesz and more general Riesz-like potentials on the whole of R^n. As a consequence, we obtain sharp Moser-Trudinger inequalities for the critical Sobolev spaces W^{a,n/a}(R^n), 0<a<n. These inequalities involve fractional Laplacians, higher order gradients, general homogeneous elliptic operators with constant coefficients, and general trace type Borel measures.

arXiv commentFinal version, to appear in Nonlinear Analysis. This paper supersedes the one in arXiv:1504.04678, referenced as [FM4], which has been divided in 2 parts. The present paper is the first part and it contains several improvements over the main original results in [FM4]. Other results in [FM4] not included here will appear in a forthcoming paper

References in corpus (3)

• Equivalence of critical and subcritical sharp Trudinger-Moser-Adams inequalities
• Sharp Adams and Moser-Trudinger inequalities on R^n and other spaces of infinite measure
• Moser functions and fractional Moser-Trudinger type inequalities