Slobodeckij空间中的复合算子

IF 0.4 4区数学 Q4 MATHEMATICS

Publicationes Mathematicae-Debrecen Pub Date : 2022-07-01 DOI:10.5486/pmd.1992.40.1-2.12

N. Merentes

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引用次数: 0

摘要

所谓Riesz类Ap = Ap(a, b)是Riesz在[5]中以如下方式引入的:定义在不一定有界开区间(a, b)上的函数u，当且仅当u在区间(a, b)上绝对连续且其导数u '属于空间Lp(a, b)时，属于1 < p <∞的类Ap，并证明了类Ap的以下表征:定义在区间(A, b)上的函数u属于类Ap，当且仅当存在一个常数K > 0，使得对于任意系统{(ai, bi)∧(A, b)}，存在一对不相交有界区间

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The operator of composition in Slobodeckij spaces

The so-called Riesz class Ap = Ap(a, b) was introduced by Riesz in [5] in the following way: A function u defined in the not necessarily bounded open interval (a, b), belongs to the class Ap with 1 < p < ∞ if and only if u is absolutely continuous in the interval (a, b) and its derivative u′ belongs to the space Lp(a, b). In the same paper, the following characterization of the class Ap was proved: A function u defined in the interval (a, b) belongs to the class Ap if and only if there exists a constant K > 0 such that for any system {(ai, bi) ⊂ (a, b)} of pairwise disjoint bounded intervals we have

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来源期刊

Publicationes Mathematicae-Debrecen 数学-数学

CiteScore

1.10

自引率

16.70%

发文量

审稿时长

6 months

期刊介绍： Publicationes Mathematicae Debrecen appears quarterly and publishes original research papers on pure mathematical topics. It welcomes contributed papers that develop interesting, or important, new mathematical ideas and results or solve outstanding problems. All papers are refereed for correctness and suitability for publication. Publicationes Mathematicae Debrecen is covered by the Mathematical Reviews, Zentralblatt fur Mathematik, Scopus, the Web of Science, the Science Abstracts and the Science Citation Index.