Mixed radial-angular bounds for a class of integral operators on Heisenberg groups

TL;DR

This paper establishes sharp bounds for various integral operators on Heisenberg groups within mixed radial-angular spaces, advancing understanding of their boundedness and spectral properties.

Contribution

It introduces new sharp bounds for linear eigenvalue operators, Hilbert operators, and Hardy-Littlewood-Pólya operators in mixed radial-angular spaces on Heisenberg groups.

Findings

Proved sharp bounds for linear transformation eigenvalue operators.

Established bounds for Hilbert and Hardy-Littlewood-Pólya operators.

Enhanced understanding of operator behavior in mixed radial-angular spaces.

Abstract

In this paper, we will prove the sharp bounds of various operators in mixed radial angular spaces on Heisenberg groups. It mainly includes the boundedness of linear transformation eigenvalue operator in mixed radial angular space; Sharp Bounds of Hilbert Operator and Hardy-Littlewood-P$\acute{o}$lya Operator in mixed radial-angular space