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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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On the $L^ 2$ inequalities involving trigonometric polynomials and their derivatives
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by Weiyu Chen PDF
Trans. Amer. Math. Soc. 347 (1995), 1753-1761 Request permission

Abstract:

In this note we study the upper bound of the integral \[ \int _0^\pi {{{({t^{(k)}}(x))}^2}w(x)} dx\] where $t(x)$ is a trigonometric polynomial with real coefficients such that $\left \| t \right \|\infty \leqslant 1$ and $w(x)$ is a nonnegative function defined on $[0,\pi ]$. When $w(x) = \sin ^jx$, where $j$ is a positive integer, we obtain the exact upper bound for the above integral.
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Additional Information
  • © Copyright 1995 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 347 (1995), 1753-1761
  • MSC: Primary 42A05; Secondary 41A17
  • DOI: https://doi.org/10.1090/S0002-9947-1995-1254834-7
  • MathSciNet review: 1254834