Atomic decompositions in Hardy spaces on bounded lipschitz domains
The theory of Hardy spaces on Rn has been generalized to Hardy spaces of distributions f on certain closed subsets F of Rn. In this paper we present some new results for the case when F is bounded and the boundary is locally Lipschitzian.
Let f have its support contained in F. If a suitable maximal function of f belongs to Lp, then f belongs to the local Hardy space hp(F). Moreover, if f belongs to the standard Hardy space on Rn, then f has an atomic decomposition whose atoms are supported in F.
KeywordsHardy Space Maximal Function Atomic Decomposition Bound LIPSCHITZ Domain Markov Inequality
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