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Strong summability of Fourier series and generalized Morrey spaces

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Abstract

We discuss some questions on strong summability of Fourier series in the context of periodic generalized Morrey spaces. By using periodic Lizorkin–Triebel–Morrey spaces as well as periodic Nikol’skij–Besov–Morrey spaces we are able to derive some if and only if assertions in this field. In addition we derive some conclusions on the local regularity of functions in terms of generalized Hölder–Zygmund spaces. Finally, we characterize the asymptotic behaviour of the approximation numbers with respect to the identity mapping from periodic Nikol’skij–Besov–Morrey spaces into the space of continuous functions.

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Authors and Affiliations

  1. Eurasian National University named after L. N. Gumilyov, Satpayev street 2, 010008, Astana, Kazakhstan

    Z. Baituyakova

  2. Institute of Mathematics, Friedrich-Schiller-University Jena, Ernst-Abbe-Platz 2, D-07743, Jena, Germany

    W. Sickel

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  1. Z. Baituyakova
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  2. W. Sickel
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Correspondence to W. Sickel.

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Baituyakova, Z., Sickel, W. Strong summability of Fourier series and generalized Morrey spaces. Anal Math 43, 371–414 (2017). https://doi.org/10.1007/s10476-017-0401-4

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  • DOI: https://doi.org/10.1007/s10476-017-0401-4

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