Mixed radial-angular bounds for Hardy-type operators on Heisenberg group

Abstract

In this paper, we study $ n $-dimensional Hardy operator and its dual in mixed radial-angular spaces on Heisenberg group and obtain their sharp bounds by using the rotation method. Furthermore, the sharp bounds of $ n $-dimensional weighted Hardy operator and weighted Cesàro operator are also obtained.

Keywords

• hardy operator
• dual operator
• weighted hardy operator
• weighted cesàro operator
• mixed radial-angular space
• heisenberg group