Strongly singular convolution operators on the Heisenberg group
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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.References
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Additional Information
- Neil Lyall
- Affiliation: Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706
- Address at time of publication: Department of Mathematics, The University of Georgia, Boyd GSRC, Athens, Georgia 30602
- MR Author ID: 813614
- Email: lyall@math.wisc.edu, lyall@math.uga.edu
- Received by editor(s): November 12, 2004
- Received by editor(s) in revised form: October 10, 2005
- Published electronically: April 16, 2007
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 359 (2007), 4467-4488
- MSC (2000): Primary 42B20, 43A80
- DOI: https://doi.org/10.1090/S0002-9947-07-04187-6
- MathSciNet review: 2309194