Abstract
In this talk we consider the analogue of Kohn’s operator but with a point singularity, P = BB∗ +B∗(t2` + x)B, B = Dx + ix Dt. We show that this operator is hypoelliptic and Gevrey hypoelliptic in a certain range, namely k < `q, with Gevrey index `q `q−k = 1 + k `q−k . Outside the above range of the parameters, i.e. when k ≥ `q, the operator is not even hypoelliptic.
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