卡诺群上的特殊测度族

Pub Date : 2022-09-18 DOI:10.1515/agms-2022-0148

B. Franchi, I. Markina

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引用次数: 0

摘要

摘要研究了具有消失p p -模的卡诺群上的测度族，我们称之为M p {M＿p} -{例外族。我们得到了通过一个公共点的本征Lipschitz曲面族为M p M＿p的充分必要条件- }p{≥1 p }{}\ge 1{例外}。对于p∈(0，∞)p {}\in\left (0, \infty)，我们描述了一类广义的M p M＿p -例外内禀Lipschitz曲面。

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Exceptional families of measures on Carnot groups

Abstract We study the families of measures on Carnot groups that have vanishing p p -module, which we call M p {M}_{p} -exceptional families. We found necessary and sufficient Conditions for the family of intrinsic Lipschitz surfaces passing through a common point to be M p {M}_{p} -exceptional for p ≥ 1 p\ge 1 . We describe a wide class of M p {M}_{p} -exceptional intrinsic Lipschitz surfaces for p ∈ ( 0 , ∞ ) p\in \left(0,\infty ) .

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