$L^{p}$–$L^{q}$ OFF-DIAGONAL ESTIMATES FOR THE ORNSTEIN–UHLENBECK SEMIGROUP: SOME POSITIVE AND NEGATIVE RESULTS. Issue 1 (6th February 2017)

• Record Type: Journal Article
• Authors: AMENTA, ALEX; TEUWEN, JONAS
• Is Part Of: Bulletin of the Australian Mathematical Society. Volume 96:Issue 1(2017)
• Page Start: 154
• Page End: 161
• Publication Date: 2017-02-06
• Subjects: primary 47D06, -- secondary 43A99; Ornstein–Uhlenbeck semigroup, -- off-diagonal estimates, -- Mehler kernel; Mathematics -- Societies, etc; Mathematics -- Periodicals; 510.5
• DOI: 10.1017/S0004972716001386
• Languages: English
• ISSNs: 0004-9727

Abstract

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.