On the boundedness of Riesz potential operators: insights from net spaces

Nursultanov E. Suragan D. Zaighum M.A.
January 2025 Tuncer ACAR

Constructive Mathematical Analysis
2025 #8 Issue 3 165 - 175 pp.

This paper investigates the boundedness of Riesz potential operators on net spaces that are structured around special nets. We use the construction of net spaces and their intrinsic properties to establish conditions under which the considered operators are bounded. The methodology developed here provides a framework for establishing Hardy–Littlewood–Sobolev inequalities on net spaces, aiming at a deeper understanding of potential theory in nonstandard settings.

Hardy–Littlewood–Sobolev inequality , local nets , net spaces , Riesz potential

Text of the article Перейти на текст статьи

Lomonosov Moscow State University, Department Of Mathematics And Informatics, Kazakhstan Branch, Astana, Kazakhstan
Institute Of Mathematics And Mathematical Modelling, Almaty, Kazakhstan
Nazarbayev University, Department Of Mathematics, 53 Kabanbay Batyr Ave, Astana, 01000, Kazakhstan
Riphah International University Department Of Mathematics And Statistics, Sector I-14, Islamabad, Pakistan

Lomonosov Moscow State University
Institute Of Mathematics And Mathematical Modelling
Nazarbayev University
Riphah International University Department Of Mathematics And Statistics

10 лет помогаем публиковать статьи Международный издатель

Книга Публикация научной статьи Волощук 2026 Book Publication of a scientific article 2026