Hardy-Littlewood-Sobolev inequality revisit on Heisenberg group

2025/09/15 by Sun, Chuhan, Wang, Zipeng
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2509.11828

Abstract

We study a family of fractional integral operators defined on Heisenberg groups. The kernels of these operators satisfy Zygmund dilations. We obtain a Hardy-Littlewood-Sobolev type inequality.

Citations

• Sharp constants in several inequalities on the Heisenberg group
• A note on discrete fractional integral operators on the Heisenberg group

Related

• Stein-Weiss inequality revisit on Heisenberg group
• Fractional integrals associated with Zygmund dilations
• Fractional Caffarelli-Kohn-Nirenberg type inequalities on the Heisenberg group
• Sharp constants in several inequalities on the Heisenberg group
• Existence of maximizers for Hardy-Littlewood-Sobolev inequalities on the Heisenberg group