1 results
$L^{p}$–
$L^{q}$ OFF-DIAGONAL ESTIMATES FOR THE ORNSTEIN–UHLENBECK SEMIGROUP: SOME POSITIVE AND NEGATIVE RESULTS
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 96 / Issue 1 / August 2017
- Published online by Cambridge University Press:
- 06 February 2017, pp. 154-161
- Print publication:
- August 2017
-
- Article
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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.
