Strongly singular integral operators associated to different quasi-norms on the Heisenberg group

In this article we study the behavior of strongly singular integrals associated to three different, albeit equivalent, quasi-norms on Heisenberg groups; these quasi-norms give rise to phase functions whose mixed Hessians may or may not drop rank along suitable varieties. In the particular case of the Koranyi norm we improve on the arguments in \cite{N1} and obtain sharp $L^2$ estimates for the associated operators.

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Published 1 January 2007