## $L^ p$ inequalities for entire functions of exponential type

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- by Qazi I. Rahman and G. Schmeisser
- Trans. Amer. Math. Soc.
**320**(1990), 91-103 - DOI: https://doi.org/10.1090/S0002-9947-1990-0974526-4
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## Abstract:

Let $f$ be an entire function of exponential type $\tau$ belonging to ${L^p}$ on the real line. It has been known since a long time that \[ \int _{ - \infty }^\infty {{{\left | {fâ(x)} \right |}^p}dx \leq {\tau ^p}\int _{ - \infty }^\infty {{{\left | {f(x)} \right |}^p}dx\quad {\text {if}}\;p \geq 1.} } \] We prove that the same inequality holds also for $0 < p < 1$. Various other estimates of the same kind have been obtained.## References

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## Bibliographic Information

- © Copyright 1990 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**320**(1990), 91-103 - MSC: Primary 30D15
- DOI: https://doi.org/10.1090/S0002-9947-1990-0974526-4
- MathSciNet review: 974526