Strongly singular convolution operators on the Heisenberg group

• Autores: Neil Lyall
• Localización: Transactions of the American Mathematical Society, ISSN 0002-9947, Vol. 359, Nº 9, 2007, págs. 4467-4488
• Idioma: inglés
• DOI: 10.1090/s0002-9947-07-04187-6
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• Resumen

  • 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.