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September 17, 2025Open Access

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

Key Points

Establishing boundedness of Riesz potential operators enhances understanding of potential theory in unique contexts.
Key conditions for boundedness are derived from the structural properties of net spaces and their construction.
The developed methodology also sheds light on Hardy–Littlewood–Sobolev inequalities relevant to net spaces.
Insights may influence future research on potential theory, particularly in non-standard environments.

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.

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

Key Points

Abstract

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