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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality 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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An example in the theory of hypercontractive semigroups
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by Andrzej Korzeniowski and Daniel W. Stroock PDF
Proc. Amer. Math. Soc. 94 (1985), 87-90 Request permission

Abstract:

Let $L = x({d^2}/d{x^2}) + (1 - x)(d/dx)$ on ${C_c}((0,\infty ))$ be the Laguerre operator. It is shown that for $t > 0$, and $1 < p < q < \infty ,\;{e^{tl}}:{L^p}({e^{ - x}}dx) \to {L^q}({e^{ - x}}dx)$ has norm 1 if and only if ${e^{ - t}} \leqslant (p - 1)/(q - 1)$ and the corresponding logarithmic Sobolev constant is not equal to $2/\lambda$, where $\lambda$ is the smallest nonzero eigenvalue of $L$.
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Additional Information
  • © Copyright 1985 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 94 (1985), 87-90
  • MSC: Primary 47D05; Secondary 47B38
  • DOI: https://doi.org/10.1090/S0002-9939-1985-0781062-0
  • MathSciNet review: 781062