2017/12/06 by Chen, Bo-Yong
#Analysis of PDEs (math.AP) #Complex Variables (math.CV) #FOS: Mathematics
paper · doi:10.48550/arxiv.1712.02044
This paper is devoted to various applications of Hardy-Sobolev type inequalities. We derive a new L2 estimate for the ∂-equation on \mathbb Cn which yields a quantitative generalization of the Hartogs extension theorem to the case when the singularity set is not necessary compact. We show that for any negative subharmonic function ψ on \mathbb Rn, n>2, the BMO norm of log |ψ| is bounded above by 2√(n-2) and |ψ|γ satisfies a reverse Hölder inequality for every 0