Note on Fourier inequalities

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Abstract

We prove that the Hausdorff--Young inequality \|f\|ₐ () C \|f\|₏ () with q (x) =p' (1/x) and p () even and non-decreasing holds in variable Lebesgue spaces if and only if p is a constant. However, under the additional condition on monotonicity of f, we obtain a full characterization of Pitt-type weighted Fourier inequalities in the classical and variable Lebesgue setting.

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Saucedo et al. (Sun,) studied this question.

synapsesocial.com/papers/68e6128fb6db6435875a52f0 https://doi.org/https://doi.org/10.48550/arxiv.2407.05503

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