Strong summability of Fourier series and generalized Morrey spaces. (English) Zbl 1399.42009
Summary: 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.
MSC:
| 42A16 | Fourier coefficients, Fourier series of functions with special properties, special Fourier series |
| 42B35 | Function spaces arising in harmonic analysis |
| 46E35 | Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems |
Keywords:
periodic Morrey space; maximal function; periodic Lizorkin-Triebel-Morrey space; periodic Nikol’skij-Besov-Morrey space; strong summability; approximation number of embeddings into \(L_1\)References:
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