## Balls and metrics defined by vector fields. I: Basic properties.(English)Zbl 0578.32044

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.
Reviewer: J.Burbea

### MSC:

 32F45 Invariant metrics and pseudodistances in several complex variables 32W05 $$\overline\partial$$ and $$\overline\partial$$-Neumann operators 65H10 Numerical computation of solutions to systems of equations 58J40 Pseudodifferential and Fourier integral operators on manifolds 32A40 Boundary behavior of holomorphic functions of several complex variables

Zbl 0517.32002
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### References:

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