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Zeitschrift für Analysis und ihre Anwendungen


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Volume 34, Issue 1, 2015, pp. 109–125
DOI: 10.4171/ZAA/1531

Published online: 2015-01-08

Moduli of Smoothness Related to Fractional Riesz-Derivatives

Konstantin V. Runovski[1] and Hans-Jürgen Schmeisser[2]

(1) Lomonosov State University, Sevastopol, Ukraine
(2) Friedrich-Schiller-University, Jena, Germany

New moduli of smoothness $\omega_{\langle \beta \rangle}(f, \delta)_p$, $0<\beta<1$, related to the Riesz derivative of order $\beta$ are introduced. Their properties are studied in $L_p$-spaces of $2\pi$-periodic functions for $0

Keywords: Trigonometric approximation, direct and converse theorems, moduli of smoothness, $K$-functionals, Riesz means

Runovski Konstantin, Schmeisser Hans-Jürgen: Moduli of Smoothness Related to Fractional Riesz-Derivatives. Z. Anal. Anwend. 34 (2015), 109-125. doi: 10.4171/ZAA/1531