Estimates of the best approximations of the functions of the Nikol’skii–Besov class in the generalized space of Lorentz
Akishev G.
1 January 2021Birkhauser
Advances in Operator Theory
2021#6Issue 1
In this paper, we consider the generalized Lorentz space of periodic functions of several variables and the Nikol’skii–Besov space of functions. The article establishes a sufficient condition for a function to belong from one generalized Lorentz space to another space in terms of the difference of the partial sums of the Fourier series of a given function. Exact in order estimates of the best approximation by trigonometric polynomials of functions of the Nikol’skii–Besov class are obtained.
Besov class , Best approximation , Logarithmic smoothness , Lorentz space
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L. N. Gumilyov Eurasian National University, Nur-Sultan, 100008, Kazakhstan
Ural Federal University, Yekaterinburg, 620002, Russian Federation
L. N. Gumilyov Eurasian National University
Ural Federal University
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