TY - JOUR AU - Elst, A. F. M. Ter AU - Prado, Humberto PY - 2002/06/01 Y2 - 2024/03/29 TI - Gaussian bounds for reduced heat kernels of subelliptic operators on nilpotent Lie groups JF - MATHEMATICA SCANDINAVICA JA - Math. Scand. VL - 90 IS - 2 SE - Articles DO - 10.7146/math.scand.a-14373 UR - https://www.mscand.dk/article/view/14373 SP - 251-266 AB - We obtain Gaussian estimates for the kernels of the semigroups generated by a class of subelliptic operators $H$ acting on $L_p(\boldsymbol R^k)$. The class includes anharmonic oscillators and Schrödinger operators with external magnetic fields. The estimates imply an $H_\infty$-functional calculus for the operator $H$ on $L_p$ with $p \in \langle 1,\infty\rangle$ 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. ER -