An Upper Bound for the Poisson Kernel on Higher Rank NA Groups

被引：6

作者：

Penney, Richard C. ^{[2
]}

Urban, Roman ^{[1
]}

机构：

[1] Univ Wroclaw, Inst Math, PL-50384 Wroclaw, Poland

[2] Purdue Univ, Dept Math, W Lafayette, IN 47907 USA

来源：

POTENTIAL ANALYSIS | 2011年 / 35卷 / 04期

关键词：

Poisson kernel; Harmonic functions; Solvable Lie groups; Higher rank NA groups; Homogeneous group; Left invariant operators; Brownian motion; DERIVATIVES; OPERATORS; MANIFOLDS;

D O I：

10.1007/s11118-010-9217-6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let S be a semi direct product S = N (sic) A where N is a connected and simply connected nilpotent Lie group and A is isomorphic with R-k, k > 1. We obtain an upper bound for the Poisson kernel for the class of second order left-invariant differential operators on S.

引用

页码：373 / 386

页数：14

共 15 条

[1] An Upper Bound for the Poisson Kernel on Higher Rank NA Groups
Richard C. Penney
Roman Urban
Potential Analysis, 2011, 35 : 373 - 386
[2] ESTIMATES FOR THE POISSON KERNEL ON HIGHER RANK NA GROUPS
Penney, Richard
Urban, Roman
COLLOQUIUM MATHEMATICUM, 2010, 118 (01) : 259 - 281
[3] Upper Bound for the Heat Kernel on Higher-Rank NA Groups
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Urban, Roman
JOURNAL OF LIE THEORY, 2013, 23 (03) : 655 - 667
[4] Estimates for the Derivatives of the Poisson Kernel on Nilpotent Meta-Abelian Groups
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[5] Estimates for the Derivatives of the Poisson Kernel on Nilpotent Meta-Abelian Groups
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Roman Urban
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[6] Liouville theorems for an integral system with Poisson kernel on the upper half space
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Science China(Mathematics), 2016, 59 (07) : 1367 - 1382
[7] Liouville theorems for an integral system with Poisson kernel on the upper half space
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SCIENCE CHINA-MATHEMATICS, 2016, 59 (07) : 1367 - 1382
[8] POISSON TRANSFORM FOR HIGHER-RANK GRAPH ALGEBRAS AND ITS APPLICATIONS
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[9] Liouville theorems for an integral system with Poisson kernel on the upper half space
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Xiang Zhang
Science China Mathematics, 2016, 59 : 1367 - 1382
[10] Local rigidity of affine actions of higher rank groups and lattices
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ANNALS OF MATHEMATICS, 2009, 170 (01) : 67 - 122

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