ABSTRACT
This chapter introduces the families of fractional Cauchy transforms. It presents a case that corresponds to the set of Cauchy transforms of measures on the unit circle and recalls some facts about the Hardy spaces and the harmonic classes. The chapter discusses the properties of complex-valued measures on the unit circle. Subsequently, these properties are shown to be related to properties of functions in Cauchy transforms. The chapter also presents Riesz-Herglotz formula and shows the correspondence between measures and functions to be one-to-one.
