L2 and Hp boundedness of strongly singular operators and oscillating operators on Heisenberg groups

TL;DR

This paper investigates the boundedness of strongly singular and oscillating convolution operators on the Heisenberg group, providing sharp L^2 results and extending to Hardy spaces.

Contribution

It establishes sharp L^2 boundedness results for strongly singular operators and introduces boundedness properties of oscillating operators on the Heisenberg group, including Hardy spaces.

Findings

Sharp L^2 boundedness results for strongly singular operators.

Boundedness properties of oscillating convolution operators.

Extension of boundedness results to Hardy spaces.

Abstract

In the first part, we obtain sharp results for L^2 boundedness of strongly singular operators on the Heisenberg group. We also define the oscillating convolution operators on the Heisenberg group and study their boundedness properties. In the second part, we obtain the boundedness on Hardy spaces.