$L^{p}$–$L^{q}$ OFF-DIAGONAL ESTIMATES FOR THE ORNSTEIN–UHLENBECK SEMIGROUP: SOME POSITIVE AND NEGATIVE RESULTS. Issue 1 (6th February 2017) - AMENTA, ALEX; TEUWEN, JONAS
Abstract : We investigate $L^{p}(\unicode[STIX]{x1D6FE})$ – $L^{q}(\unicode[STIX]{x1D6FE})$ 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.