– OFF-DIAGONAL ESTIMATES FOR THE ORNSTEIN–UHLENBECK SEMIGROUP: SOME POSITIVE AND NEGATIVE RESULTS
2017 ◽
Vol 96
(1)
◽
pp. 154-161
◽
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.
2016 ◽
Vol 19
(04)
◽
pp. 1650030
◽
Keyword(s):
1974 ◽
Vol 133
(3)
◽
pp. 432-436
◽
Keyword(s):
Keyword(s):