Lipschitz measures and vector-valued Hardy spaces
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 HXp(ℝn), 0<p<1. We also prove that all these measures have Lipschitz densities. This im...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2001-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171201004549 |
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| Summary: | 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 HXp(ℝn), 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 HXp(ℝn)∗ can be identified with a space of
Lipschitz functions with values in X*. |
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| ISSN: | 0161-1712 1687-0425 |