International Journal of Mathematics and Mathematical Sciences
Volume 25 (2001), Issue 5, Pages 345-356

Lipschitz measures and vector-valued Hardy spaces

Magali Folch-Gabayet,1 Martha Guzmán-Partida,2 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

Received 24 January 2000

Copyright © 2001 Magali Folch-Gabayet et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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(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 HXp(n) can be identified with a space of Lipschitz functions with values in X*.