F-algebras of holomorphic functions in a half-plane defined by maximal functions

Metric and structural properties of F-algebras of holomorphic functions in a half-plane defined in terms of maximal functions are studied. The properties under examination include boundary properties, surjective isometry groups, and characteristics of bounded and compact subsets. The interest in properties of analytic functions in a half-plane has significantly increased after Hille and Tamarkin's work, which was provoked by Paley and Wiener's study of the Fourier transform. The extensive use of functional analysis methods in the theory of analytic functions has extended the functional-algebraic point of view.