Gaussian bounds for reduced heat kernels of subelliptic operators on nilpotent Lie groups

A. F. M. Ter Elst, Humberto Prado

Abstract


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.

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DOI: http://dx.doi.org/10.7146/math.scand.a-14373

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ISSN 0025-5521 (print) ISSN 1903-1807 (online)

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