Image of Lp(ℝn) under the Hermite Semigroup

The Heat Equation for the Hermite Operator on the Heisenberg Group∗

We give a formula for the one-parameter strongly continuous semigroup e−tL, t > 0, generated by the Hermite operator L on the Heisenberg group H1 in terms of Weyl transforms, and use it to obtain an L2 estimate for the solution of the initial value problem for the heat equation governed by L in terms of the Lp norm of the initial data for 1 ≤ p ≤ ∞. This research has been partially supported by...

Estimates for the Maximal Operator of the Ornstein-uhlenbeck Semigroup

We show pointwise estimates for the maximal operator of the Ornstein-Uhlenbeck semigroup for functions that are integrable with respect to the Gaussian measure. The estimates are used to prove pointwise convergence. The Ornstein-Uhlenbeck semigroup is defined by Ttf(x)= [ k(t,x,y)f(y)dy, Jr" where ,1. \ -"/2m -2f,-«/2 / \e~'x-y\ \ 4 ^ _ ^ D« k(t, x, y) n (1 -e ) exp -■-Z^L, t > 0, x £ R . This ...

The Structure and Amenability of L^p-Munn Algebras

Lp-analyticity of Schrödinger semigroups on Riemannian manifolds

We address the problems of extrapolation, analyticity, and Lp-spectral independence for C0-semigroups in the abstract context of metric spaces with exponentially bounded volume. The main application of the abstract result is Lp-analyticity of angle π 2 of Schrödinger semigroups on Riemannian manifolds with Ricci curvature bounded below, under the condition of form smallness of the negative part...

Module contractibility for semigroup algebras

In this paper, we nd the relationships between module contractibility of aBanach algebra and its ideals. We also prove that module contractibility ofa Banach algebra is equivalent to module contractibility of its module uniti-zation. Finally, we show that when a maximal group homomorphic image ofan inverse semigroup S with the set of idempotents E is nite, the moduleprojective tensor product l1...