Multi-parameter fractional integration on Heisenberg group

2025/10/15 by Chuhan Sun, Sun, Chuhan, Zipeng Wang +1
Mathematics · #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Fractional Differential Equations Solutions #Mathematical and Theoretical Analysis #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2510.13411

openalex publication_date 2025/10/15 · openalex created_date 2025/10/17 · openalex updated_date 2026/07/28

Abstract

We study strong fractional maximal operator and fractional integral operator associated with Zygmund dilation defined on Heisenberg group. Characterizations are established for the L^p to L^q regularity of these two operators.

Citations

• Kato-Ponce estimates for fractional sublaplacians
• Sharp constants in several inequalities on the Heisenberg group
• A note on discrete fractional integral operators on the Heisenberg group

Related

• A class of singular integrals associated with Zygmund dilations
• Hardy-Littlewood-Sobolev inequality revisit on Heisenberg group
• Stein-Weiss inequality revisit on Heisenberg group
• Weighted estimates for bilinear fractional integral operator on the Heisenberg group
• Fractional integrals associated with Zygmund dilations