TY - JOUR T1 - Local Hardy Spaces and Inhomogeneous Dirichlet Problems in Exterior Regular Domains 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).