补径向奇异函数张成空间的正则子空间的插值

IF 0.7 3区数学 Q2 MATHEMATICS

Studia Mathematica Pub Date : 2022-01-01 DOI:10.5445/IR/1000134315

Konstantin Zerulla

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引用次数: 2

摘要

我们分析了正则函数组成的子空间的和与具有r^\ α $型奇点的函数张成的空间的插值问题。特别地，我们确定了所有插值参数，对于这些参数，正则函数的子空间的插值空间仍然是闭子空间。这里的主要工具是伊凡诺夫和卡尔顿对子空间插值的结果。为了应用它，我们研究了奇异函数r^ α $的K$泛函。结果表明，K泛函的上界和下界在零处有一个共同的衰减率。

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Interpolation of a regular subspace complementing the span of a radially singular function

We analyze the interpolation of the sum of a subspace, consisting of regular functions, with the span of a function with $r^\alpha$-type singularity. In particular, we determine all interpolation parameters, for which the interpolation space of the subspace of regular functions is still a closed subspace. The main tool is here a result by Ivanov and Kalton on interpolation of subspaces. To apply it, we study the $K$-functional of the $r^\alpha$-singular function. It turns out that the $K$-functional possesses upper and lower bounds that have a common decay rate at zero.

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来源期刊

Studia Mathematica 数学-数学

CiteScore

1.50

自引率

12.50%

发文量

审稿时长

5 months

期刊介绍： The journal publishes original papers in English, French, German and Russian, mainly in functional analysis, abstract methods of mathematical analysis and probability theory.