Convolution-type operators in grand Lorentz spaces
Nursultanov E.D. Rafeiro H. Suragan D.
June 2025Birkhauser
Analysis and Mathematical Physics
2025#15Issue 3
We introduce and study a novel grand Lorentz space—that we believe is appropriate for critical cases—that lies “between” the Lorentz–Karamata space and the recently defined grand Lorentz space from Ahmed et al. (Mediterr J Math 17:57, 2020). We prove both Young’s and O’Neil’s inequalities in the newly introduced grand Lorentz spaces, which allows us to derive a Hardy–Littlewood–Sobolev-type inequality. We also discuss Köthe duality for grand Lorentz spaces, from which we obtain a new Köthe dual space theorem in grand Lebesgue spaces.
Dual space , Grand Lorentz space , Hardy–Littlewood–Sobolev inequality , Interpolation theorem
Text of the article Перейти на текст статьи
Department of Mathematics and Informatics, Lomonosov Moscow State University, Kazakhstan Branch, Astana, Kazakhstan
Institute of Mathematics and Mathematical Modelling, Almaty, Kazakhstan
Department of Mathematical Sciences, College of Science, United Arab Emirates University, Al Ain, PO Box 15551, United Arab Emirates
Department of Mathematics, Nazarbayev University, 53 Kabanbay Batyr Ave, Astana, 010000, Kazakhstan
Department of Mathematics and Informatics
Institute of Mathematics and Mathematical Modelling
Department of Mathematical Sciences
Department of Mathematics
10 лет помогаем публиковать статьи Международный издатель
Книга Публикация научной статьи Волощук 2026 Book Publication of a scientific article 2026