A parametrix for step-two hypoelliptic diffusion equations

Taylor, Thomas

doi:10.1090/S0002-9947-1986-0837807-X

A parametrix for step-two hypoelliptic diffusion equations
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by Thomas Taylor

Trans. Amer. Math. Soc. 296 (1986), 191-215

DOI: https://doi.org/10.1090/S0002-9947-1986-0837807-X

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Abstract:

In this paper I construct a parametrix for the hypoelliptic diffusion equations $(\partial /\partial t - L)u = 0$, where $L = \sum \nolimits _{a = 1}^n {g_a^2}$ and where the ${g_a}$ are vector fields which satisfy the property that they, together with all of the commutators $[{g_{a,}}{g_b}]$ for $a < b$, are at each point linearly independent and span the tangent space.

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