Интерполяционные теоремы для нелинейных операторов в общих пространствах типа Морри и их приложения

2021

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DOI 10.4213/tm4129
Data confidence 70 medium
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Abstract

Доказаны новые интерполяционные теоремы для достаточно широкого класса нелинейных операторов в пространствах типа Морри. В частности, эти теоремы применимы к интегральным операторам Урысона. Получены аналоги интерполяционных теорем Марцинкевича-Кальдерона, Стейна-Вейса, Петре. Установлен критерий $(p,q)$-квазислабой ограниченности оператора Урысона.