Poincar\'e- and Sobolev- type inequalities for complex $m$-Hessian equations
Complex Variables
2020-04-24 v2 Analysis of PDEs
Functional Analysis
Abstract
By using quasi-Banach techniques as key ingredient we prove Poincar\'e- and Sobolev- type inequalities for -subharmonic functions with finite -energy. A consequence of the Sobolev type inequality is a partial confirmation of B\l ocki's integrability conjecture for -subharmonic functions.
Cite
@article{arxiv.1908.10135,
title = {Poincar\'e- and Sobolev- type inequalities for complex $m$-Hessian equations},
author = {Per Ahag and Rafal Czyz},
journal= {arXiv preprint arXiv:1908.10135},
year = {2020}
}