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- W2963084232 abstract "Let $Omega$ be a strongly Lipschitz domain of $mathbb{R}^n$, whose complement in $mathbb{R}^n$ is unbounded. Let $L$ be a second order divergence form elliptic operator on $L^2 (Omega)$ with the Dirichlet boundary condition, and the heat semigroup generated by $L$ having the Gaussian property $(G_{mathrm{diam}(Omega)})$ with the regularity of its kernels measured by $muin(0,1]$, where $mathrm{diam}(Omega)$ denotes the diameter of $Omega$. Let $Phi$ be a continuous, strictly increasing, subadditive and positive function on $(0,infty)$ of upper type 1 and of strictly critical lower type $p_{Phi}in(n/(n+mu),1]$. In this paper, the authors introduce the Orlicz–Hardy space $H_{Phi,,r}(Omega)$ by restricting arbitrary elements of the Orlicz–Hardy space $H_{Phi}(mathbb{R}^n)$ to $Omega$ and establish its atomic decomposition by means of the Lusin area function associated with ${e^{-tL}}{tge0}$. Applying this, the authors obtain two equivalent characterizations of $H{Phi,,r}(Omega)$ in terms of the nontangential maximal function and the Lusin area function associated with the heat semigroup generated by $L$." @default.
- W2963084232 created "2019-07-30" @default.
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- W2963084232 date "2013-01-01" @default.
- W2963084232 modified "2023-10-03" @default.
- W2963084232 title "Real-variable characterizations of Orlicz–Hardy spaces on strongly Lipschitz domains of $mathbb{R}^n$" @default.
- W2963084232 doi "https://doi.org/10.4171/rmi/719" @default.
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