On extreme points of the unit ball of a Hardy-Lorentz space

TL;DR

This paper characterizes the extreme points of the unit ball in Hardy-Lorentz spaces, providing new necessary and sufficient conditions, especially for functions that are products of outer functions and Blaschke factors.

Contribution

It introduces novel criteria for identifying extreme points in Hardy-Lorentz spaces, advancing the understanding of their geometric structure.

Findings

Derived new necessary and sufficient conditions for extreme points.

Provided detailed characterization for functions as products of outer functions and Blaschke factors.

Enhanced the theoretical framework for Hardy-Lorentz space geometry.

Abstract

We investigate the problem of a characterization of extreme points of the unit ball of a Hardy-Lorentz space $H(\Lambda(\varphi))$, posed by Semenov in 1978. New necessary and sufficient conditions, under which a normalized function $f$ in $H(\Lambda(\varphi))$ belongs to this set, are found. The most complete results are obtained in the case when $f$ is the product of an outer analytic function and a Blaschke factor.