Duality of vector valued Hardy spaces

Author(s)

Fábio José Bertoloto

• Document type: Doctoral Thesis
• Institution: Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática
• Defense date: 2009-10-03

Examining board members

Mário Carvalho de Matos; Sergio Antonio Tozoni; Luiza Amalia de Moraes; Daniela Mariz Silva Vieira

• Advisor: Jorge Tulio Mujica Ascui

Abstract

In this work we study the vector-valued Hardy spaces Hp(Delta ; F) (1 = p = 8). We also study the Banach spaces with the properties ARNP and RNP and the UMD spaces. We also study the Banach spaces with the RNP and ARNP properties, and also the UMD spaces. By following the approach of Taylor [36],[37] in the scalar-valued case, we prove that, when F and F' have the ARNP property, when (Hp(Delta ; F))' and Hq(Delta ; F) are canonically topologically isomorphic (for 1 < p, q < 8, 1/ p + 1/ q = 1) if and only if F is UMD (AU)