Title: Singular integrals operators on Hardy spaces
Abstract: The real variable theory of the Hardy spaces represents a fruitful setting for
the study of singular integral operators. In fact, it is because of the failure of these
operators to preserve the space of integrable functions, that the Hardy space assumes
its prominent role in harmonic analysis. We will present the definition and basic
properties of Hardy spaces. We will discuss the atomic decomposition, dual spaces,
interpolation properties, and the behavior of singular integral operators acting on
Hardy spaces and their duals.