Strongly singular convolution operators on the Heisenberg group

Lyall, Neil

doi:10.1090/S0002-9947-07-04187-6

Strongly singular convolution operators on the Heisenberg group
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by Neil Lyall PDF

Trans. Amer. Math. Soc. 359 (2007), 4467-4488 Request permission

Abstract:

We consider the $L^2$ mapping properties of a model class of strongly singular integral operators on the Heisenberg group $\mathbf {H}^n$; these are convolution operators on $\mathbf {H}^n$ 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.

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