Two-point inequalities, the Hermite semigroup and the Gauss-Weierstrass semigroup
Two-point inequalities, the Hermite semigroup and the Gauss-Weierstrass semigroup
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两点不等式、Hermite 半群和 Gauss-Weierstrass 半群
DOI：
10.1016/0022-1236(79)90080-6
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发表时间：
1979
影响因子：
1.7
通讯作者：
F. Weissler
中科院分区：
文献类型：
--
作者：
F. Weissler
设−zH，Rez ≠ 0，是R上具有高斯测度μ的Hermite半群。给出了− zH是从Lp（μ）到Lq（μ），1 <$p，q <$∞的有界映射的充要条件，并在许多情况下证明了−zH：Lp（μ）→Lq（μ）实际上是一个压缩映射.此外，这些结果和一个将Hermite半群与Gauss-Weierstrass半群z Δ联系起来的公式，使我们能够在许多情况下精确计算z Δ：Lp（dx）→Lq（dx）的范数.
Lete−zH, Rez⩾ 0, be the Hermite semigroup onRwith Gauss measure μ. Necessary and sufficient conditions fore−zHto be a bounded map fromLp(μ) intoLq(μ), 1 ⩽p,q⩽ ∞, are found and in many cases it is proved thate−zH:Lp(μ) →Lq(μ) is in fact a contraction. Furthermore, these results and a formula relating the Hermite semigroup with the Gauss-Weierstrass semigroupezΔenable one to calculate the precise norm ofezΔ:Lp(dx) →Lq(dx) in a large number of cases.