This article is cited in 2 papers

Methods of trigonometric approximation and generalized smoothness. II

S. Artamonov^a, K. Runovski^b, H.-J. Schmeisser<sup>c

a</sup> National Research University Higher School of Economics, Moscow, Russian Federation
^b Lomonosov Moscow State University, Moscow, Russian Federation
^c Friedrich-Schiller University, Jena, Germany

Abstract: The paper deals with the equivalence of approximation errors in $L_p$-spaces ($0<p<\infty$) with respect to approximation processes, generalized $K$-functionals and appropriate moduli of smoothness. The results are used to derive various characterizations of periodic Besov spaces by means of constructive approximation and moduli of smoothness. The main focus lies on spaces $\mathbb{B}_{p,q}^s(\mathbb{T}^d)$, where $0 < p < 1$, $0 < q \leqslant\infty$ and $s > 0$.

Keywords and phrases: trigonometric approximation, summability, $K$-functionals, moduli of smoothness, periodic Besov spaces.

MSC: 46E35, 42A10, 42B35, 41A17

Received: 01.10.2022

Language: English

DOI: 10.32523/2077-9879-2022-13-4-18-43

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