Volume 14, Issue 1
Local Hardy Spaces and Inhomogeneous Dirichlet Problems in Exterior Regular Domains
DOI:

J. Part. Diff. Eq., 14 (2001), pp. 1-11.

Published online: 2001-02

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• Abstract

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).

• Keywords

Exterior regular domain local Hardy space Hölder space inhomogeneous Dirichlet problem Green potential