Strong summability of Fourier series and Morrey spaces

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• 作者：Merey Sautbekova (1)
  Winfried Sickel (2)
  
• 刊名：Analysis Mathematica
• 出版年：2014
• 出版时间：March 2014
• 年：2014
• 卷：40
• 期：1
• 页码：31-62
• 全文大小：345 KB
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• 作者单位：Merey Sautbekova (1)
  Winfried Sickel (2)
  
  1. Eurasian National University named after L.N. Gumilyov, Munaytpasov str. 5, Astana, 010000, Kazakhstan
  2. Institute of Mathematics, Friedrich-Schiller-University Jena, Ernst-Abbe-Platz 2, D-07743, Jena, Germany
  
• ISSN：1588-273X

文摘

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 H?lder-Zygmund spaces. In the final section, we study consequences for strong summability of Fourier series.