Hardy type inequalities in the category of hausdorff operators

Classical Hardy’s inequalities are concerned with the Hardy operator and its adjoint, the Bellman operator. Hausdorff operators in their various forms are natural generalizations of these two operators. In this paper, we try to adjust the scheme used by Bradley for Hardy’s inequalities with general weights to the Hausdorff setting. It is not surprising that the obtained necessary conditions differ from the sufficient conditions as well as that both depend not only on weights but also on the kernel that generate the Hausdorff operator. For the Hardy and Bellman operators, the obtained necessary and sufficient conditions coincide and reduce to the classical ones. © Springer Nature Switzerland AG 2019.

Авторы
Сборник материалов конференции
Издательство
Springer New York LLC
Язык
Английский
Страницы
81-91
Статус
Опубликовано
Том
291
Год
2019
Организации
  • 1 Department of Mathematics, Bar-Ilan University, Ramat-Gan, 52900, Israel
  • 2 S.M. Nikol’skii Institute of Mathematics RUDN University, 6 Miklukho-Maklay St, Moscow, 117198, Russian Federation
Ключевые слова
Hardy inequality; Hausdorff operator
Дата создания
24.12.2019
Дата изменения
24.12.2019
Постоянная ссылка
https://repository.rudn.ru/ru/records/article/record/55335/