Taylor formula for homogenous groups and applications
Taylor formula for homogenous groups and applications
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DOI：
10.1007/s00209-008-0372-z
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发表时间：
2009-06-01
影响因子：
0.8
通讯作者：
Bonfiglioli, Andrea
中科院分区：
文献类型：
--
作者：
Bonfiglioli, Andrea
本文给出了齐次群在Folland和Stein(Hardy空间)意义下的带整余项的Taylor公式。数学笔记，第28卷。普林斯顿大学出版社，普林斯顿，1982)。这个公式使我们能够给出所谓的‘泰勒不等式’的一个简化证明。作为副产品，我们给出了相关的泰勒多项式的显式表达式。提供了应用程序。其中，给出了高阶导数(在李代数意义下)满足适当增长条件的函数实可解的一个充分条件。此外，当L是齐次群上的一般齐次左不变微分算子时，我们证明了与“L调和”函数有关的泰勒多项式的“L调和”性。(这一结果是获得与L相关的Schauder估计的要素之一)。
In this paper, we provide a Taylor formula with integral remainder in the setting of homogeneous groups in the sense of Folland and Stein (Hardy spaces on homogeneous groups. Mathematical notes, vol 28. Princeton University Press, Princeton, 1982). This formula allows us to give a simplified proof of the so-called 'Taylor inequality'. As a by-product, we furnish an explicit expression for the relevant Taylor polynomials. Applications are provided. Among others, it is given a sufficient condition for the real-analiticity of a function whose higher order derivatives (in the sense of the Lie algebra) satisfy a suitable growth condition. Moreover, we prove the 'L-harmonicity' of the Taylor polynomials related to a 'L-harmonic' function, when L is a general homogenous left-invariant differential operator on a homogeneous group. (This result is one of the ingredients for obtaining Schauder estimates related to L).