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([STIX]x1D6FE) – L^q([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.