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

2025/07/17 by С. В. Асташкин, Astashkin, Sergey V.
Mathematics · #30H10 #30J05 #46A55 #46B22 #46E30 #Advanced Harmonic Analysis Research #FOS: Mathematics #Functional Analysis (math.FA) #Geometric Analysis and Curvature Flows #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.2507.12810

openalex publication_date 2025/07/17 · openalex created_date 2025/10/14 · openalex updated_date 2026/07/28

Abstract

We investigate the problem of a characterization of extreme points of the unit ball of a Hardy-Lorentz space H(Λ(φ)), posed by Semenov in 1978. New necessary and sufficient conditions, under which a normalized function f in H(Λ(φ)) 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.

Citations

• On the set of extreme points of the unit ball of a Hardy-Lorentz space
• A note on extreme points of the unit of Hardy-Lorentz spaces
• Questions about extreme points
• Interpolation of linear operators

Related

• A note on extreme points of the unit of Hardy-Lorentz spaces
• On the set of extreme points of the unit ball of a Hardy-Lorentz space
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• Questions about extreme points
• Functions with small and large spectra as (non)extreme points in subspaces of H^∞