Resumen de Strongly singular convolution operators on the Heisenberg group

Neil Lyall

• We consider the L2 mapping properties of a model class of strongly singular integral operators on the Heisenberg group Hn; these are convolution operators on Hn whose kernels are too singular at the origin to be of Calderón-Zygmund type. This strong singularity is compensated for by introducing a suitably large oscillation. Our results are obtained by utilizing the group Fourier transform and uniform asymptotic forms for Laguerre functions due to Erdélyi.