Strongly singular convolution operators on the Heisenberg group
Author:
Neil Lyall
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
Published electronically:
April 16, 2007
MathSciNet review:
2309194
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: We consider the 
mapping properties of a model class of strongly singular integral operators on the Heisenberg group 
; these are convolution operators on 
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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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
Email:
lyall@math.wisc.edu, lyall@math.uga.edu
DOI:
https://doi.org/10.1090/S0002-9947-07-04187-6
Received by editor(s):
November 12, 2004
Received by editor(s) in revised form:
October 10, 2005
Published electronically:
April 16, 2007
Article copyright:
© Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.