拟共形分析中一类映射的泛函和解析性质

IF 0.8 3区数学 Q2 MATHEMATICS

Izvestiya Mathematics Pub Date : 2021-01-01 DOI:10.1070/IM9082

S. Vodopyanov, A. Tomilov

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引用次数: 1

摘要

我们定义了空间域的同胚的双指标尺度，其几何描述是由目标空间中聚光器的-容量的行为控制来决定的，该行为是根据源空间中聚光器的加权-容量来决定的。基于由中映射的逆导出的复合算子(从加权Sobolev空间到非加权Sobolev空间)的性质，我们得到了一个等价的泛函和解析描述。当，映射类与在过去25年中被广泛研究的所谓的-同胚集合一致时。

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Functional and analytic properties of a class of mappings in quasi-conformal analysis

We define a two-index scale , , of homeomorphisms of spatial domains in , the geometric description of which is determined by the control of the behaviour of the -capacity of condensers in the target space in terms of the weighted -capacity of condensers in the source space. We obtain an equivalent functional and analytic description of based on the properties of the composition operator (from weighted Sobolev spaces to non-weighted ones) induced by the inverses of the mappings in . When , the class of mappings coincides with the set of so-called -homeomorphisms which have been studied extensively in the last 25 years.

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来源期刊

Izvestiya Mathematics 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： The Russian original is rigorously refereed in Russia and the translations are carefully scrutinised and edited by the London Mathematical Society. This publication covers all fields of mathematics, but special attention is given to: Algebra; Mathematical logic; Number theory; Mathematical analysis; Geometry; Topology; Differential equations.