Abstract
We establish for 0<p<1 the analog of the Bernstein- Zygmund inequality for the derivative of a trigonometric polynomial We prove weighted inequalities, exact in the sense of order, for trigonometric polynomials and their derivatives in various integral metrics with exponents 0<p, q≤∞.
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Translated from Matematicheskie Zametki, Vol. 18, No. 4, pp. 489–498, October, 1975.
In conclusion, the author thanks S. B. Stechkin for his help in this work.
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Iva, V.I. Certain inequalities in various metrics for trigonometric polynomials and their derivatives. Mathematical Notes of the Academy of Sciences of the USSR 18, 880–885 (1975). https://doi.org/10.1007/BF01153038
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DOI: https://doi.org/10.1007/BF01153038