Balls and metrics defined by vector fields. I: Basic properties
type: Item
instance of: scholarly article
title: Balls and metrics defined by vector fields. I: Basic properties
zbMATH Open document ID: 0578.32044
DOI: 10.1007/BF02392539
author: Alexander Nagel
author: Stephen Wainger
author: Elias M. Stein
published in: Acta Mathematica
publication date: 1985-01-01T00:00:00Z
review text: The authors study the basic properties of certain balls and metrics that are naturally induced from a given family of vector fields. These properties are used to obtain estimates for the kernels of approximate inverses of some non-elliptic partial differential operators, such as Hörmander's sum of squares. Some of the present properties were announced earlier by the authors in Proc. Natl. Acad. Sci. USA 78, 6596-6599 (1981; Zbl 0517.32002). In that paper, they also announced applications of these balls and metrics to problems concerning the boundary behavior of holomorphic functions in domains of finite type. The details of these applications will, according to the authors, appear in another paper.
reviewed by: Jacob Burbea
Mathematics Subject Classification ID: 32F45
Mathematics Subject Classification ID: 32W05
Mathematics Subject Classification ID: 65H10
Mathematics Subject Classification ID: 58J40
Mathematics Subject Classification ID: 32A40
zbMATH DE Number: 3925275
zbMATH Keywords: non-isotropic ball
zbMATH Keywords: hypoelliptic operator
zbMATH Keywords: exponential map
zbMATH Keywords: Campbell- Hausdorff formula
zbMATH Keywords: metrics
zbMATH Keywords: boundary behavior of holomorphic functions
MaRDI profile type: Publication
cites work: Q3281164
cites work: Q3852412
cites work: Q5339349
cites work: Hypoelliptic second order differential equations
cites work: Boundary behavior of functions holomorphic in domains of finite type
cites work: Hypoelliptic differential operators and nilpotent groups
cites work: Q5607484
cites work: Boundary Behavior of Holomorphic Functions of Several Complex Variables. (MN-11)
full work available at URL: https://doi.org/10.1007/bf02392539
OpenAlex ID: W2024626650
description: scientific article; zbMATH DE number 3925275