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In this article, we establish Gaussian decay for the Box_b-heat kernel onpolynomial models in C^2. Our technique attains the exponential decay via apartial Fourier transform. On the transform side, the problem becomes findingquantitative smoothness estimates on a heat kernel associated to the weighteddbar-operator on L^2(C). The bounds are established with Duhamel's formula andcareful estimation.

Heat Kernels, Smoothness Estimates, and Exponential Decay