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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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