The complex interpolation of Lebesgue spaces $L^{p_0}$ and $L^{p_1}$ are well-known, that is, $[L^{p_0}, L^{p_1}]_\theta = L^p$, where $(1-\theta)/p_0+1/p_1 = 1/p$ for some $\theta \in [0,1]$.
Now I would like to find the complex interplation space $[L^{p_0} , \mathcal{F}L^{p_1}]_\theta$, where $\|f\|_{\mathcal{F}L^p} := \|\mathcal{F}f\|_{L^p}$ and $\mathcal{F}$ is the Fourier transform.
Does anyone know about this topic?
