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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| _version_ | 1832552314115719168 |
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| author | Magali Folch-Gabayet Martha Guzmán-Partida Salvador Pérez-Esteva |
| author_facet | Magali Folch-Gabayet Martha Guzmán-Partida Salvador Pérez-Esteva |
| author_sort | Magali Folch-Gabayet |
| collection | DOAJ |
| description | 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*. |
| format | Article |
| id | doaj-art-aa21a80e2c2446ea8dc6a973550ff68d |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2001-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-aa21a80e2c2446ea8dc6a973550ff68d2025-02-03T05:59:08ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252001-01-0125534535610.1155/S0161171201004549Lipschitz measures and vector-valued Hardy spacesMagali Folch-Gabayet0Martha Guzmán-Partida1Salvador Pérez-Esteva2Instituto de Matemáticas, Universidad Nacional Autónoma de México, Ciudad Universitaria, D.F., 04510, MexicoUniversidad de Sonora, Departamento de Matemáticas, Blvd. Luis Encinas y Rosales, Hermosillo, Sonora 83000, MexicoInstituto de Matemáticas, Universidad Nacional Autónoma de México, Unidad Cuernavaca Apartado Postal 273-3, Administración de Correos #3, Cuernavaca, Morelos 62251, MexicoWe 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*.http://dx.doi.org/10.1155/S0161171201004549 |
| spellingShingle | Magali Folch-Gabayet Martha Guzmán-Partida Salvador Pérez-Esteva Lipschitz measures and vector-valued Hardy spaces International Journal of Mathematics and Mathematical Sciences |
| title | Lipschitz measures and vector-valued Hardy spaces |
| title_full | Lipschitz measures and vector-valued Hardy spaces |
| title_fullStr | Lipschitz measures and vector-valued Hardy spaces |
| title_full_unstemmed | Lipschitz measures and vector-valued Hardy spaces |
| title_short | Lipschitz measures and vector-valued Hardy spaces |
| title_sort | lipschitz measures and vector valued hardy spaces |
| url | http://dx.doi.org/10.1155/S0161171201004549 |
| work_keys_str_mv | AT magalifolchgabayet lipschitzmeasuresandvectorvaluedhardyspaces AT marthaguzmanpartida lipschitzmeasuresandvectorvaluedhardyspaces AT salvadorperezesteva lipschitzmeasuresandvectorvaluedhardyspaces |