International Journal of Mathematics and Mathematical Sciences
Volume 25 (2001), Issue 5, Pages 345-356
doi:10.1155/S0161171201004549
Lipschitz measures and vector-valued Hardy spaces
Magali Folch-Gabayet1
, Martha Guzmán-Partida2
and Salvador Pérez-Esteva3
1Instituto de Matemáticas, Universidad Nacional Autónoma de México, Ciudad Universitaria, D.F., 04510, Mexico
2Universidad de Sonora, Departamento de Matemáticas, Blvd. Luis Encinas y Rosales, Hermosillo 83000, Sonora, Mexico
3Instituto de Matemáticas, Universidad Nacional Autónoma de México, Unidad Cuernavaca Apartado Postal 273-3, Administración de Correos #3, Cuernavaca 62251, Morelos, Mexico
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 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*.