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ON SOME CLASS OF EXTREME POINTS OF THE UNIT BALL OF A HARDY-LORENTZ SPACE
- Authors: Astashkin S.V.1,2,3
-
Affiliations:
- Samara National Research University
- Lomonosov Moscow State University, Moscow Сenter of Fundamental and Applied Mathematics
- Bahcesehir University
- Issue: Vol 522, No 1 (2025)
- Pages: 3-6
- Section: MATHEMATICS
- URL: https://journal-vniispk.ru/2686-9543/article/view/296211
- DOI: https://doi.org/10.31857/S2686954325020016
- EDN: https://elibrary.ru/HYWTQE
- ID: 296211
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Abstract
The problem of a characterization of the set of extreme points of the unit ball in the Hardy-Lorentz space H(Λ(φ)), posed by E.M. Semenov in 1978, is considered. 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.
About the authors
S. V. Astashkin
Samara National Research University; Lomonosov Moscow State University, Moscow Сenter of Fundamental and Applied Mathematics; Bahcesehir University
Email: astash@ssau.ru
Moscow, Russia; Moscow, Russia; Istanbul, Turkey
References
- K. de Leeuw, W. Rudin, Extreme points and extreme problems in H1, Pacific J. Math., 8 (1958), 467–485.
- К. Гофман, Банаховы пространства аналитических функций. М.: Изд-во иностр. литер., 1963.
- И.Б. Брыскин, А.А. Седаев, О геометрических свойствах единичного шара в пространствах типа классов Харди, Зап. научн. сем. ЛОМИ, 39 (1974), 7–16. https://doi.org/10.1007/BF01455319
- S.V. Astashkin, On the set of extreme points of the unit ball of a Hardy-Lorentz space, Math. Zeitschrift (2025) 310:51. https://doi.org/10.1007/s00209-025-03763-1
- Исследования по линейным операторам и теории функций, 99 нерешенных задач линейного и комплексного анализа, Зап. научн. сем. ЛОМИ, 81, ред. Н.К. Никольский, В.П. Хавин, С.В. Хрущев, Изд-во “Наука”, Ленинград. отд., Л., 1978, 296 с.
- Linear and Complex Analysis. Problem Book. 199 Research Problems, V.P. Khavin, S.V. Khrushchev, N.K. Nikol’skii, eds., Lecture Notes in Mathematics 1043, Springer-Verlag, Berlin, 1984.
- Linear and Complex Analysis. Problem Book 3. Part I, V.P. Khavin, N.K. Nikol’skii, eds., Lecture Notes in Mathematics 1573, SpringerVerlag, Berlin, 1994.
- С.Г. Крейн, Ю.И. Петунин, Е.М. Семенов, Интерполяция линейных операторов. М.: Наука, 1978.
- J. Lindenstrauss, L. Tzafriri, Classical Banach Spaces, II. Function Spaces. Springer-Verlag, Berlin–New York, 1979.
- N.L. Carothers, S.J. Dilworth and D.A. Trautman, On the geometry of the unit sphere of the Lorentz space Lw,1, Glasgow Math. J., 34 (1992), 21–25.
- N.L. Carothers, B. Turett, Isometries on Lp,1, Trans. Amer. Math. Soc., 297 (1986), 95–103.
- П. Кусис, Введение в теорию пространств Hp. М.: Мир, 1984.
- Б.С. Кашин, А.А. Саакян, Ортогональные ряды. М.: Изд-во АФЦ, 1999.
- J. Carrillo-Alanı´s, G.P. Curbera, A note on extreme points of the unit ball of Hardy-Lorentz spaces, Proc. Amer. Math. Soc., 152 (2024), 2551–2554.
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