Estimates of the Fourier widths of the classes of periodic functions with given majorant of the mixed modulus of smoothness. (English. Russian original) Zbl 1480.42002
Sib. Math. J. 59, No. 2, 217-230 (2018); translation from Sib. Mat. Zh. 59, No. 2, 277-292 (2018).
Summary: We obtain some order-sharp estimates for the Fourier widths of Nikol’skii-Besov and Lizorkin-Triebel function classes with given majorant of the mixed modulus of smoothness in the Lebesgue space for a few relations between the parameters of the class and the space. The upper bounds follow from estimates of the approximation of functions of these classes by special partial sums of their Fourier series with respect to the multiple system of periodized Meyer wavelets.
MSC:
| 42A10 | Trigonometric approximation |
| 42A24 | Summability and absolute summability of Fourier and trigonometric series |
| 41A46 | Approximation by arbitrary nonlinear expressions; widths and entropy |
| 42C40 | Nontrigonometric harmonic analysis involving wavelets and other special systems |
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