2-POINT INEQUALITIES, THE HERMITE SEMIGROUP, AND THE GAUSS-WEIERSTRASS SEMIGROUP

被引：34

作者：

WEISSLER, FB

机构：

[1] Department of Mathematics, The University of Texas, Austin

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 1979年 / 32卷 / 01期

关键词：

D O I：

10.1016/0022-1236(79)90080-6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let e-zH, Re z ≥ 0, be the Hermite semigroup on R with Gauss measure μ. Necessary and sufficient conditions for e-zH to be a bounded map from Lp(μ) into Lq(μ), 1 ≤ p, q ≤ ∞, are found and in many cases it is proved that e-zH: Lp(μ) → Lq(μ) is in fact a contraction. Furthermore, these results and a formula relating the Hermite semigroup with the Gauss-Weierstrass semigroup ezΔ enable one to calculate the precise norm of ezΔ:Lp(dx) → Lq(dx) in a large number of cases. © 1979.

引用

页码：102 / 121

页数：20

共 6 条

[1] BEST CONSTANTS IN YOUNGS INEQUALITY, ITS CONVERSE, AND ITS GENERALIZATION TO MORE THAN 3 FUNCTIONS [J].