Session S05 - Advances on Spaces of Non-absolutely Integrable Functions and Related Applications

Monday, July 12, 13:10 ~ 13:40 UTC-3

On the equivalence between Weak BMO and the space of derivatives of the Zygmund class

Eddy Kwessi

Trinity University, USA   -   ekwessi@tyrinity.edu

In this paper, we will discuss the space of functions of weak bounded mean oscillation. In particular, we will show that this space is the dual space of the special atom space, whose dual space was already known to be the space of derivative of functions (in the sense of distribution) belonging to the Zygmund class of functions. We show in particular that this proves that the Hardy space $H^1$ strictly contains the space special atom space.

View abstract PDF