Some scales of equivalent weight characterizations of Hardy's inequality: The case q < p

We consider the weighted Hardy inequality (∫0 ∞ (∫0 x f(t)dt)q u(x)dx)1/q ≤ C(∫0 ∞ f p(x)v(x)dx)1/p for the case 0 < q < p < ∝, p > 1. The weights u(x) and v(x) for which this inequality holds for all f (x) ≥ 0 may be characterized by the Mazya-Rosin or by the Persson-Stepanov conditions. In this paper, we show that these conditions are not unique and can be supplemented by some continuous scales of conditions and we prove their equivalence. The results for the dual operator which do not follow by duality when 0 < q < 1 are also given. © ELEMENT.

Авторы
Persson L.-E.1 , Stepanov V. 2 , Wall P.1
Издательство
Element D.O.O.
Номер выпуска
2
Язык
Английский
Страницы
267-279
Статус
Опубликовано
Том
10
Год
2007
Организации
  • 1 Department of Mathematics, Luleå University of Technology, SE-971 87 Luleå, Sweden
  • 2 Department of Mathematical Analysis, Peoples' Friendship University of Russia, Miklukho-Maklai 6, Moscow 117198, Russian Federation
Ключевые слова
Integral inequalities; Weighted Hardy's inequality
Дата создания
19.10.2018
Дата изменения
19.10.2018
Постоянная ссылка
https://repository.rudn.ru/ru/records/article/record/3282/