TY - JOUR
T1 - Local Hardy Spaces and Inhomogeneous Dirichlet Problems in Exterior Regular Domains
AU - Henggeng Wang  & Houyu Jia 
JO - Journal of Partial Differential Equations
VL - 1
SP - 1
EP - 11
PY - 2001
DA - 2001/02
SN - 14
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jpde/5464.html
KW - Exterior regular domain
KW - local Hardy space
KW - Hölder space
KW - inhomogeneous Dirichlet problem
KW - Green potential
AB -  In this paper, firstly we give an atomic decomposition of the local Hardy spaces h^p_r(Ω)(O < p ≤ 1) and their dual spaces. where the domain Ω is exterior regular in R^n(n ≥ 3). Then for given data f ∈ h^p_r(Ω), we discuss the inhomogeneous Dirichlet problems: {Lu = f \quad in Ω u = 0 \qquad on ∂ Ω where the operator L is uniformly elliptic. Also we obtain the estimation of Green potential in the local Hardy spaces h^p_r(Ω).