Some general properties of operators in Morrey-type spaces

In the paper we consider general properties of operators acting from rearrangement invariant spaces into generalized Morrey-type spaces. We extract wide class of operators that preserve non-negativity and monotonicity of functions and prove two-sided estimates for their norms. As corollaries we obtain corresponding results for operators of embedding and for Hardy–Littlewood maximal operators. For operators commuting with a shift operator the results are extended to the case of global Morrey-type spaces. As an application of these approaches we establish a criterion of the embedding for a weighted Lorentz space into a Morrey-type space. © Springer Nature Switzerland AG 2019.

Авторы
Сборник материалов конференции
Издательство
Springer New York LLC
Язык
Английский
Страницы
3-34
Статус
Опубликовано
Том
291
Год
2019
Организации
  • 1 Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St, Moscow, 117198, Russian Federation
  • 2 Steklov Mathematical Institute of Russian Academy of Sciences, 8 Gubkina St., Moscow, 119991, Russian Federation
Ключевые слова
Banach function spaces; Criterion of embedding; Decreasing rearrangements; Estimates of the norms; Local and global Morrey-type spaces; Lorentz spaces; Rearrangement invariant spaces
Дата создания
24.12.2019
Дата изменения
24.12.2019
Постоянная ссылка
https://repository.rudn.ru/ru/records/article/record/55336/