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A Decay Property of the Fourier Transform and its Application to the Stokes Problem

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Abstract.

We prove an optimal relationship between the regularity of a function and the asymptotic behavior of its Fourier transform. As an application of this result we show L p -estimates for the Stokes semigroup in \( \Bbb R^n \) and \( {\Bbb R}_+^n \) when \( 1\leqq p\leqq \infty \).

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Authors and Affiliations

  1. Department of Mathematical Sciences, School of Science and Engineering, Waseda University, Ohkubo 3-4-1, Shinjyuku-ku, Tokyo 169-8555, Japan, e-mail: yshibata@mn.waseda.ac.jp, , , , , , JP

    Y. Shibata

  2. Faculty of Engineering, Shizuoka University, Hamamatsu 432-8561, Japan, e-mail: tssshim@eng.shizuoka.ac.jp, , , , , , JP

    S. Shimizu

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  1. Y. Shibata
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  2. S. Shimizu
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Accepted: August 29, 2000

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Shibata, Y., Shimizu, S. A Decay Property of the Fourier Transform and its Application to the Stokes Problem. J. math. fluid mech. 3, 213–230 (2001). https://doi.org/10.1007/PL00000970

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  • DOI: https://doi.org/10.1007/PL00000970

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