Let be a strongly Lipschitz domain of , whose complement in is unbounded. Let be a second order divergence form elliptic operator on with the Dirichlet boundary condition, and the heat semigroup generated by having the Gaussian property with the regularity of its kernels measured by , where denotes the diameter of . Let be a continuous, strictly increasing, subadditive and positive function on of upper type 1 and of strictly critical lower type . In this paper, the authors introduce the Orlicz–Hardy space by restricting arbitrary elements of the Orlicz–Hardy space to and establish its atomic decomposition by means of the Lusin area function associated with . Applying this, the authors obtain two equivalent characterizations of in terms of the nontangential maximal function and the Lusin area function associated with the heat semigroup generated by .
Cite this article
Dachun Yang, Sibei Yang, Real-variable characterizations of Orlicz–Hardy spaces on strongly Lipschitz domains of . Rev. Mat. Iberoam. 29 (2013), no. 1, pp. 237–292DOI 10.4171/RMI/719