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

Year 2025, Volume: 8 Issue: 3, 165 - 175, 15.09.2025

Erlan Nursultanov Durvudkhan Suragan Muhammad Asad Zaighum

https://doi.org/10.33205/cma.1716123

Abstract

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 non-standard settings.

Keywords

Riesz Potential , Hardy–Littlewood–Sobolev inequality , Net spaces , Local nets

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