Symbols and orbits for 3-step nilpotent Lie groups |
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Authors: | G Ratcliff |
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Institution: | Department of Mathematics, University of Missouri-St. Louis St. Louis, Missouri 63121 USA |
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Abstract: | Sufficient conditions are derived for L2-boundedness of a convolution operator on a 3-step nilpotent Lie group. This is achieved by producing estimates on the Kirillov symbol of the operator, and is closely linked to the co-adjoint orbit structure of the group. A structure theorem for 3-step nilpotent Lie groups with 1-dimensional center is proved. |
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