On inequalities of periodic functions and their derivatives

Author:
Z. Ditzian

Journal:
Proc. Amer. Math. Soc. **87** (1983), 463-466

MSC:
Primary 26D10

MathSciNet review:
684640

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Abstract: The inequality is proved for many spaces of periodic functions. An analogue for sequences is also given.

**[1]**Edwin F. Beckenbach and Richard Bellman,*Inequalities*, Ergebnisse der Mathematik und ihrer Grenzgebiete, N. F., Bd. 30, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1961. MR**0158038****[2]**Richard Bellman,*A note on periodic functions and their derivatives*, J. London Math. Soc.**18**(1943), 140–142. MR**0009965****[3]**Z. Ditzian,*Some remarks on inequalities of Landau and Kolmogorov*, Aequationes Math.**12**(1975), no. 2/3, 145–151. MR**0380503****[4]**Ky Fan, Olga Taussky, and John Todd,*Discrete analogs of inequalities of Wirtinger*, Monatsh. Math.**59**(1955), 73–90. MR**0070676****[5]**A. Kolmogoroff,*On inequalities between the upper bounds of the successive derivatives of an arbitrary function on an infinite interval*, Amer. Math. Soc. Translation**1949**(1949), no. 4, 19. MR**0031009****[6]**D. G. Northcott,*Some inequalities between periodic functions and their derivatives*, J. London Math. Soc.**14**(1939), 198–202. MR**0000417**

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DOI:
https://doi.org/10.1090/S0002-9939-1983-0684640-0

Article copyright:
© Copyright 1983
American Mathematical Society