Strong summability of Fourier series and Morrey spacesСильная суммируемость рядов Фурье в пространствах Морри

被引：0
作者：
Merey Sautbekova
Winfried Sickel
机构：
[1] Eurasian National University named after L.N. Gumilyov,Institute of Mathematics
[2] Friedrich-Schiller-University Jena,undefined
来源：
Analysis Mathematica | 2014年 / 40卷 / 1期
关键词：
Fourier Series; Besov Space; Strong Approximation; Morrey Space; Strong Summability;
D O I：
10.1007/s10476-014-0104-z
中图分类号：
学科分类号：
摘要：
This work is dedicated to the investigation of strong summability of Fourier series in the context of periodic Morrey spaces. First, we study the Hilbert transform in the periodic vector-valued context. Boundedness of the Hilbert transform implies uniform estimates of the operator norms of the partial sums of the Fourier series. Afterwards, we study the Lizorkin-Triebel-Morrey and Nikol’skij-Besov-Morrey spaces. Here we concentrate on Lizorkin representations and embeddings into the scale of Hölder-Zygmund spaces. In the final section, we study consequences for strong summability of Fourier series.
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页码：31 / 62
页数：31
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