Families of functions with equal-power absolutely continuous integrals

  • A. A. Dovgoshei Ин-т прикл. математики и механики АН Украины, Донецк

Abstract

The approximation of functions from Hardy classes by bounded analytic functions is investigated. A theorem is proved, characterizing the sets of functions with equiabsolutely continuous integrals as limit points of the family of bounded subsets of the space Н∞.

References

Федорчук В. В., Филиппов В. В. Общая топология.— М. : Изд-во Моск, ун-та, 1988.— 252 с.

Куратовский Л. Топология: В 2-х т.— М. : Мир, 1966. — Т. 1.— 594 с.

Натансон И. П. Теория функций вещественной переменной.— М. : Наука, 1974.— 480 с.

Гарнетт Дж. Ограниченные аналитические функции.— М. : Мир, 1984.— 470 с.

Published
28.02.1992
How to Cite
Dovgoshei A. A. “Families of Functions With Equal-Power Absolutely Continuous Integrals”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 44, no. 2, Feb. 1992, pp. 178-84, https://umj.imath.kiev.ua/index.php/umj/article/view/7830.
Issue
Vol 44 No 2 (1992)
Section
Research articles

Copyright (c) 1992 A. A. Dovgoshei

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