Gaussian bounds for reduced heat kernels of subelliptic operators on nilpotent Lie groups - Elst, A. F. M. Ter; Prado, Humberto (Mathematica Scandinavica, 2002)
We obtain Gaussian estimates for the kernels of the semigroups generated by a class of subelliptic operators H acting on L_p(R^k). The class includes anharmonic oscillators and Schrödinger operators with external magnetic fields. The estimates imply an H_∞-functional calculus for the operator H on L_p with p 1,∞ and in many cases the spectral p-independence. Moreover, we show for a subclass of operators satisfying a homogeneity property that the Riesz transforms of all orders are bounded.