Order Sharp Estimates for Monotone Operators on Orlicz–Lorentz Classes

We consider the monotone operator P, which maps Orlicz-Lorentz class into some ideal space Y=Y(R:+). Orlicz-Lorentz class is determined as the cone of Lebesgue-measurable functions on (Formula Presented) having the decreasing rearrangements that belong to weighted Orlicz space under some general assumptions concerning properties of functions (Formula Presented) and v. We prove the reduction theorems allowing reducing the estimates of the norm of operator (Formula Presented) to the estimates for its restriction on some cone of nonnegative step-functions in (Formula Presented). Application of these results to identical operator mapping (Formula Presented) into the weighted Lebesgue space (Formula Presented) gives the sharp description of the associate space for (Formula Presented). The main results of this paper were announced in, [20]. They develop the results of our paper, [19] related to the case of N-functions. © 2017, Springer Nature Singapore Pte Ltd.

Авторы
Сборник материалов конференции
Издательство
Springer New York LLC
Язык
Английский
Страницы
37-83
Статус
Опубликовано
Том
206
Год
2017
Организации
  • 1 Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St., Moscow, 117198, Russian Federation
Ключевые слова
Monotone operators; Orlic–Lorentz classes
Дата создания
19.10.2018
Дата изменения
19.10.2018
Постоянная ссылка
https://repository.rudn.ru/ru/records/article/record/5677/