Bernstein's Inequality for the Weyl Derivatives of Trigonometric Polynomials in the Space~$L_0$

A. O. Leont'eva

Matematičeskie zametki, Tome 104 (2018) no. 2, pp. 255-264.

Résumé

A logarithmic asymptotics for the behavior with respect to $n$ of the exact constant in Bernstein's inequality for the Weyl derivative of positive noninteger order of trigonometric polynomials of order $n$ in the space $L_0$ is obtained. It turns out that the order in $n$ of the behavior of this constant for positive noninteger orders of the derivatives has exponential growth in contrast to the power growth in the well-studied case of classical derivatives of positive integer order.

Détail

Keywords: trigonometric polynomial, Weyl derivative, Bernstein's inequality, the space $L_0$.

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