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The Wiener algebra $W_n$ is the image by the Fourier transform of $L^1(\mathbb R^n)$. What is the (complex) interpolation space between $W_n$ and $L^2(\mathbb R^n)$? It is probably not true that for $\theta \in (0,1)$,
$$ [W_n, L^2(\mathbb R^n)]_\theta = L^p(\mathbb R^n),\quad p=2/\theta, $$ but the homogeneity required should be the right one. Are some Besov spaces better candidates?

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  • $\begingroup$ Do you mean complex interpolation? (the real interpolation has two parameters). $\endgroup$
    – Mikael de la Salle
    Jun 10, 2015 at 7:25
  • $\begingroup$ @MikaeldelaSalle Yes, you are right. But some real interpolation result would also be interesting to me. $\endgroup$
    – Bazin
    Jun 11, 2015 at 11:42

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