TY - JOUR
T1 - LpLq Off-diagonal estimates for the Ornstein-Uhlenbeck semigroup
T2 - Some positive and negative results
AU - Amenta, Alex
AU - Teuwen, Jonas
PY - 2017
Y1 - 2017
N2 - We investigate Lp(γ)-Lq(γ) off-diagonal estimates for the Ornstein-Uhlenbeck semigroup (etL)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.
AB - We investigate Lp(γ)-Lq(γ) off-diagonal estimates for the Ornstein-Uhlenbeck semigroup (etL)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.
KW - Mehler kernel
KW - off-diagonal estimates
KW - Ornstein-Uhlenbeck semigroup
UR - http://www.scopus.com/inward/record.url?scp=85011695994&partnerID=8YFLogxK
U2 - 10.1017/S0004972716001386
DO - 10.1017/S0004972716001386
M3 - Article
AN - SCOPUS:85011695994
SN - 0004-9727
VL - 96
SP - 154
EP - 161
JO - Bulletin of the Australian Mathematical Society
JF - Bulletin of the Australian Mathematical Society
IS - 1
ER -