Orlicz-Hardy spaces associated with divergence operators on unbounded strongly Lipschitz domains of $\mathbb{R}^n$ Dachun YangShanshuang Yang 42B3042B3542B2042B2535J2542B3747B38Orlicz-Hardy spacedivergence form elliptic operatorstrongly Lipschitz domainNeumann boundary conditionGaussian propertynontangential maximal functionLusin area function Let $\Omega$ be either $\mathbb{R}^n$ or an unbounded strongly Lipschitz domain of $\mathbb{R}^n$, and let $\Phi$ be a continuous, strictly increasing, subadditive, and positive function on $(0,\infty)$ of upper type $1$ and of strictly critical lower type index $p_{\Phi}\in(n/(n+1),1]$. Let $L$ be a divergence form elliptic operator on $L^2(\Omega)$ with the Neumann boundary condition, and assume that the heat semigroup generated by $L$ has the Gaussian property $(G_{\infty})$. In this paper, the authors introduce the Orlicz-Hardy space $H_{\Phi,L}(\Omega)$ via the nontangential maximal function associated with $\{e^{-t\sqrt{L}}\}_{t\ge 0}$ and establish its equivalent characterization in terms of the Lusin area function associated with $\{e^{-t\sqrt{L}}\}_{t\ge 0}$. The authors also introduce the "geometrical" Orlicz-Hardy space $H_{\Phi,z}(\Omega)$ via the classical Orlicz-Hardy space $H_{\Phi}(\mathbb{R}^n)$ and prove that the spaces $H_{\Phi,L}(\Omega)$ and $H_{\Phi,z}(\Omega)$ coincide with equivalent norms, from which characterizations of $H_{\Phi,L}(\Omega)$, including the vertical and the nontangential maximal function characterizations associated with $\{e^{-tL}\}_{t\ge 0}$ and the Lusin area function characterization associated with $\{e^{-tL}\}_{t\ge 0}$, are deduced. All the above results generalize the well-known results of P. Auscher and E. Russ by taking $\Phi(t)\equiv t$ for all $t\in(0,\infty)$. Indiana University Mathematics Journal 2012 text pdf 10.1512/iumj.2012.61.4535 10.1512/iumj.2012.61.4535 en Indiana Univ. Math. J. 61 (2012) 81 - 129 state-of-the-art mathematics http://iumj.org/access/