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Lipschitz measures and vector-valued Hardy spaces

Author

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  • Magali Folch-Gabayet
  • Martha Guzmán-Partida
  • Salvador Pérez-Esteva

Abstract

We define certain spaces of Banach-valued measures called Lipschitz measures. When the Banach space is a dual space X * , these spaces can be identified with the duals of the atomic vector-valued Hardy spaces H X p ( ℝ n ) , 0 < p < 1 . We also prove that all these measures have Lipschitz densities. This implies that for every real Banach space X and 0 < p < 1 , the dual H X p ( ℝ n ) ∗ can be identified with a space of Lipschitz functions with values in X * .

Suggested Citation

  • Magali Folch-Gabayet & Martha Guzmán-Partida & Salvador Pérez-Esteva, 2001. "Lipschitz measures and vector-valued Hardy spaces," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 25, pages 1-12, January.
    • Handle: RePEc:hin:jijmms:397859
    DOI: 10.1155/S0161171201004549
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