The classical Hausdorff-Young inequalities for the Fourier transform acting between appropriate $L_p$ spaces are cornerstones of Fourier analysis. Here we extend it to weighted spaces of Besov or Sobolev type where the weight has the form $w(x)=(1+|x|^2)^{\alpha/2}$. This note is not a paper or draft but a sketchy complement to some earlier results where we dealt with mapping properties of the Fourier transform.
Atomic representations in function spaces and applications to pointwise multipliers and diffeomorphisms, a new approach
$B_w^u$-function spaces and their interpolation
Functional Equations and Fourier Analysis
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