Necessary and sufficient conditions for the boundedness of the maximal operator from lebesgue spaces to morrey-type spaces

It is proved that the boundedness of the maximal operator M from a Lebesgue space Lp1 (Rn) to a general local Morrey-type space LMpθ ,w(Rn) is equivalent to the boundedness of the embedding operator from Lp1 (Rn) to LMpθ ,w(Rn) and in its turn to the boundedness of the Hardy operator from L p1 p2 (0,8) to the weighted Lebesgue space L θ p2 ,v(0,8) for a certain weight function v determined by the functional parameter w. This allows obtaining necessary and sufficient conditions on the function w ensuring the boundedness of M from Lp1 (Rn) to LMp2θ ,w(Rn) for any 0> <8, 0> p2 ≤ p1 <8, p1 ≥1. These conditions with p1 = p2 =1 are necessary and sufficient for the boundedness of M from L1(R n) to the weak local Morreytype space WLM1 ,w(Rn) .

Авторы
Издательство
Element D.O.O.
Номер выпуска
2
Язык
Английский
Страницы
401-418
Статус
Опубликовано
Том
17
Год
2014
Организации
  • 1 Cardiff School of Mathematics, Cardiff University, Senghennydd Road, Cardiff, CF5 24AG, United Kingdom
  • 2 Faculty of Mechanics and Mathematics, L.N. Gumilyov Eurasian National University, 2 Mirzoyan St, 010008 Astana, Kazakhstan
  • 3 Department of Nonlinear Analysis and Optimisation, Peoples' Friendship University of Russia, 6 Miklukho Maklay St, 119634 Moscow, Russian Federation
Ключевые слова
Maximal operator; Morrey-type spaces; Weak Morrey-type spaces
Дата создания
19.10.2018
Дата изменения
19.10.2018
Постоянная ссылка
https://repository.rudn.ru/ru/records/article/record/4991/