Ultracontractivity and strong Sobolev inequality for q-Ornstein-Uhlenbeck semigroup (-1 < q < 1)

被引：30
作者：
Bozejko, M [1 ]
机构：
[1] Univ Wroclaw, Inst Math, PL-50384 Wroclaw, Poland
来源：
INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS | 1999年 / 2卷 / 02期
关键词：
D O I：
10.1142/S0219025799000114
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We prove that q-Ornstein-Uhlenbeck semigroup U-t((q)) = Gamma(q)(e(-t) I) maps L-2 into L-infinity and parallel to U(t)((q))f parallel to infinity less than or equal to C(q)t(-3/2)parallel to f parallel to(2), 0 < t < 1 for -1 < q < 1. This is an extension of Ph. Biane's(3) result on Nelson hypercontractivity and the ultracontractivity of the free (q = 0) and q-second quantization.
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页码：203 / 220
页数：18
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