A Correction to this paper has been published: https://doi.org/10.1007/s11142-021-09605-9

We study the construction of extrapolation spaces operator-valued multiplication operators on Bochner Lp-spaces by means Lp-fiber spaces.

Let $T$ be a linear operator that, for some $p_1\in(1,\infty)$, is bounded on $L^{p_1}(\tilde w)$ all $\tilde w\in A_{p_1}(\mathbb R^d)$ and in addition compact $L^{p_1}(w_1)$ $w_1\in R^d)$. Then $L^p(w)$ $p\in(1,\infty)$ $w\in A_p(\mathbb This "compact version" of Rubio de Francia's celebrated weighted extrapolation theorem follows from combination results the interpolation theory spaces one h...