R^n 上临界 Riesz 势与分数阶拉普拉斯算子的尖锐指数可积性
偏微分方程分析
2017-11-22 v2
摘要
我们推导了整个 R^n 上 Riesz 及更一般的类 Riesz 势的尖锐 Adams 不等式。作为结果，我们得到了临界 Sobolev 空间 W^{a,n/a}(R^n), 0<a<n 的尖锐 Moser-Trudinger 不等式。这些不等式涉及分数阶拉普拉斯算子、高阶梯度、具有常系数的广义齐次椭圆算子以及一般的迹型 Borel 测度。
引用
@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}
}
备注
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