Abstract
Let G be a homogeneous Lie group with a left Haar measure dg and L the action of G as left translations on Lp(G; dg). Further, let H = dL(C) denote a homogeneous operator associated with L. If H is positive and hypoelliptic on L2 we prove that it is closed on each of the Lp-spaces, p e (1, 8), and that it generates a semigroup S with a smooth kernel K which, with its derivatives, satisfies Gaussian bounds. The semigroup is holomorphic in the
open right half-plane on all the Lp-spaces, p e [1, 8]. Further extensions of these results to nonhomogeneous operators and general representations are also given.
Original language | English |
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Pages (from-to) | 197-216 |
Journal | Colloquium Mathematicum |
Volume | 67 |
Publication status | Published - 1994 |