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.
Keywords
Cite
@article{arxiv.1702.02078,
title = {Sharp exponential integrability for critical Riesz potentials and fractional Laplacians on R^n},
author = {Luigi Fontana and Carlo Morpurgo},
journal= {arXiv preprint arXiv:1702.02078},
year = {2017}
}
Comments
Final 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