English

Stein-Weiss type inequality on the upper half space and its applications

Analysis of PDEs 2023-03-14 v1

Abstract

In this paper, we establish some Stein-Weiss type inequalities with general kernels on the upper half space and study the existence of extremal functions for this inequality with the optimal constant. Furthermore, we also investigate the regularity, asymptotic estimates, symmetry and non-existence results of the positive solutions of the corresponding Euler-Lagrange integral system. As an application, we finally derive some Liouville type results for the Hartree type equations in the half space.

Keywords

Cite

@article{arxiv.2303.06979,
  title  = {Stein-Weiss type inequality on the upper half space and its applications},
  author = {Xiang Li and Zifei Shen and Marco Squassina and Minbo Yang},
  journal= {arXiv preprint arXiv:2303.06979},
  year   = {2023}
}

Comments

33 pages

R2 v1 2026-06-28T09:13:44.520Z