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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A fundamental inequality in the convolution of $L_{2}$ functions on the half line
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by Saburou Saitoh PDF
Proc. Amer. Math. Soc. 91 (1984), 285-286 Request permission

Abstract:

For any positive integer $q$ and ${F_j} \in {L_2}(0,\infty )$, we note the inequality for the iterated convolution $\prod _{j = 1}^{2q} * {F_j}\;$ of ${F_j}$: \[ \int _0^\infty {{{\left | {\prod \limits _{j = 1}^{2q} { * {F_j}(t)} } \right |}^2}{t^{1 - 2q}}dt \leqslant \frac {1}{{(2q - 1)!}}\prod \limits _{j = 1}^{2q} {\int _0^\infty {{{\left | {{F_j}(t)} \right |}^2}dt.} } } \]
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Additional Information
  • © Copyright 1984 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 91 (1984), 285-286
  • MSC: Primary 30C40; Secondary 26D20
  • DOI: https://doi.org/10.1090/S0002-9939-1984-0740187-5
  • MathSciNet review: 740187