On one inequality of Kolmogorov type for fractional derivatives

Ye.V. Turchin (Dnipropetrovsk State University)

Abstract


We prove two generalizations of Kashin-Besov inequality for fractional derivatives. The corollaries of proved theorems are some analogues of Paly theorem, which allow to give lower bounds for polynomials by orthogonal systems in $$$L_p [0, 1]$$$ spaces for $$$p \in (0, 1)$$$.

References


Bochkarev S.V. "Logarithmic growth of arithmetic means of Lebesgue functions of bounded orthonormal systems", Dokl. AN SSSR, 1987; 223(1): pp. 16-19. (in Russian)

Zygmund A. Trigonometric series. Vol 2, Mir, 1965; (in Russian)




DOI: https://doi.org/10.15421/249818

  

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Copyright (c) 1998 Ye.V. Turchin

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ISSN (Online): 2664-5009
ISSN (Print): 2664-4991
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