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
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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