Abstract
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.
Keywords
- Hardy Space
- Maximal Function
- Atomic Decomposition
- Bound LIPSCHITZ Domain
- Markov Inequality
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© 1988 Springer-Verlag
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Forsman, K. (1988). Atomic decompositions in Hardy spaces on bounded lipschitz domains. In: Cwikel, M., Peetre, J., Sagher, Y., Wallin, H. (eds) Function Spaces and Applications. Lecture Notes in Mathematics, vol 1302. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0078876
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DOI: https://doi.org/10.1007/BFb0078876
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-18905-3
Online ISBN: 978-3-540-38841-8
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