Geodesic
Bernstein's Inequality for the Weyl Derivatives of Trigonometric Polynomials in the Space~$L_0$
Matematičeskie zametki, Tome 104 (2018) no. 2, pp. 255-264

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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.
Keywords: trigonometric polynomial, Weyl derivative, Bernstein's inequality, the space $L_0$. 
@article{MZM_2018_104_2_a8,
     author = {A. O. Leont'eva},
     title = {Bernstein's {Inequality} for the {Weyl} {Derivatives} of {Trigonometric} {Polynomials} in the {Space~}$L_0$},
     journal = {Matemati\v{c}eskie zametki},
     pages = {255--264},
     publisher = {mathdoc},
     volume = {104},
     number = {2},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2018_104_2_a8/}
}
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A. O. Leont'eva. Bernstein's Inequality for the Weyl Derivatives of Trigonometric Polynomials in the Space~$L_0$. Matematičeskie zametki, Tome 104 (2018) no. 2, pp. 255-264. http://geodesic.mathdoc.fr/item/MZM_2018_104_2_a8/