Abstract

Interpolation spaces are described for spaces of functions of positive smoothness on a domain \(G\) of the Euclidean space \(\mathbb R^n\) that satisfies the flexible cone condition. As a consequence, multiplicative estimates for the norms of functions are obtained. The arguments are based on integral representations of functions over a flexible cone in terms of the local approximations of functions by polynomials and on estimates of the arising convolution operators.

中文翻译：

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域上正光滑函数空间的插值

摘要

描述了在满足弹性锥条件的欧氏空间\（\ mathbb R ^ n \）的域\（G \）上的正光滑函数空间的插值空间。结果，获得了函数范数的乘法估计。自变量基于多项式对函数的局部近似以及对出现的卷积算符的估计，基于函数在圆锥上的积分表示。