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Atomic decompositions in Hardy spaces on bounded lipschitz domains

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1302)

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

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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