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Some linear processes for Fourier series and best approximations of functions in Morrey spaces. (English) Zbl 1509.42004

Summary: In the present work we estimate of deviations of periodic functions from linear operators constructed on basis of its Fourier series in terms of the best approximation of these functions in Morrey space. Specifically, we study the problem of the effect of metric of space on order of change of deviations.

MSC:

42A10 Trigonometric approximation
42A05 Trigonometric polynomials, inequalities, extremal problems
41A10 Approximation by polynomials
41A25 Rate of convergence, degree of approximation
41A50 Best approximation, Chebyshev systems
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