Two-sided estimates of Lebesque constants for Hölder spaces

IF 0.8 3区数学 Q2 MATHEMATICS Mathematische Nachrichten Pub Date : 2024-10-22 DOI:10.1002/mana.202200286

Evgenii I. Berezhnoi

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Abstract

A two-sided estimate of Lebesgue constants is proposed for the Hölder space $H_{k}^{ω} (X)$ , constructed from the modulus of continuity of the $k$ th order calculated in the symmetric space $X$ . Choosing different function spaces $X$ , we obtain new criteria for the convergence of classical Fourier series.

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赫尔德空间的勒贝斯克常数的双侧估计值

对Hölder空间H k ω (X)$ H_k^\ ω (X)$提出了勒贝格常数的双边估计，由对称空间X$ X$中计算的k$ k$阶的连续模构造。选取不同的函数空间X$ X$，得到了经典傅里叶级数收敛性的新判据。

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来源期刊

Mathematische Nachrichten 数学-数学

CiteScore

1.50

自引率

0.00%

发文量

157

审稿时长

4-8 weeks

期刊介绍： Mathematische Nachrichten - Mathematical News publishes original papers on new results and methods that hold prospect for substantial progress in mathematics and its applications. All branches of analysis, algebra, number theory, geometry and topology, flow mechanics and theoretical aspects of stochastics are given special emphasis. Mathematische Nachrichten is indexed/abstracted in Current Contents/Physical, Chemical and Earth Sciences; Mathematical Review; Zentralblatt für Mathematik; Math Database on STN International, INSPEC; Science Citation Index

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