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We study continuity and other properties related to some kind of compactness of multiplication operators between different spaces of pth power integrable scalar functions with respect to a vector measure.

We apply the Calderón interpolation methods to Orlicz and weakly Orlicz function spaces with respect to a Banach‐space‐valued measure defined on a σ‐algebra. The results we obtain generalize those in the case of Banach lattices of p‐integrable and weakly p‐integrable functions with respect to such a vector measure.

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