Chapter Twelve

Rough estimates on the scalar heat kernel

The purpose of this chapter is to establish rough estimates on the heat kernel image for the scalar hypoelliptic operator image on image defined in chapter 11. By rough estimates, we mean just uniform bounds on the heat kernel, and not a Gaussian-like decay like in (4.5.3). Such refined estimates will be obtained in chapter 13 for bounded b, and in chapter 15 for b large. We will also obtain corresponding bounds ...

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