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We prove Calder\'on-Zygmund type estimates of weak solutions tonon-homogeneous nonlocal parabolic equations under a minimal regularityrequirement on kernel coefficients. In particular, the right-hand side ispresented by a sum of fractional Laplacian type data and a non-divergence typedata. Interestingly, even though the kernel coefficients are discontinuous, weobtain a significant increment of fractional differentiability for thesolutions, which is not observed in the corresponding local parabolicequations.

Calder\'on-Zygmund theory of nonlocal parabolic equations with discontinuous coefficients