The Szegö kernel for <i>k</i>-CF functions on the quaternionic Heisenberg group

Abstract

The tangential k-Cauchy–Fueter operator and the k-CF functions on the quaternionic Heisenberg group are quaternionic counterparts of the tangential CR operator and CR functions on the Heisenberg group in the theory of several complex valuables. We use the group Fourier transform on the quaternionic Heisenberg group to analyze the operator associated the tangential k-Cauchy–Fueter operator and to construct its kernel, from which we get the Szegö kernel of the orthogonal projection from the space of functions to the space of integrable k-CF functions on the quaternionic Heisenberg group.