$L^p$-$L^q$ off-diagonal estimates for the Ornstein–Uhlenbeck semigroup: some positive and negative results
Résumé
We investigate L^p(γ)–L^q(γ) off-diagonal estimates for the Ornstein– Uhlenbeck semigroup (e^{tL})_{t>0}. For sufficiently large t (quantified in terms of p and q) these estimates hold in an unrestricted sense, while for sufficiently small t they fail when restricted to maximal admissible balls and sufficiently small annuli. Our counterexample uses Mehler kernel estimates .
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