A fundamental theme in classical Fourier analysis relates smoothnessproperties of functions to the growth and/or integrability of their Fouriertransform. By using a suitable class of $L^{p}-$multipliers, a rather generalinequality controlling the size of Fourier transforms for large and smallargument is proved. As consequences, quantitative Riemann-Lebesgue estimatesare obtained and an integrability result for the Fourier transform is developedextending ideas used by Titchmarsh in the one dimensional setting.
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机译：经典傅里叶分析中的一个基本主题是函数的平滑度属性与其傅里叶变换的增长和/或可积性相关。通过使用合适的$ L ^ {p}-$乘数类，证明了控制大小参数的傅立叶变换的大小的相当一般性。结果，获得了定量的黎曼-勒贝格估计，并发展了傅立叶变换的可积性结果，扩展了蒂奇马什在一维环境中使用的思想。
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