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This paper provides a local and global Calder\'on-Zygmund type estimate of aweak solution to the parabolic double-phase system. The proof of local estimateis based on comparison estimates and the scaling invariant property of theparabolic double-phase system in the intrinsic cylinders of the stopping timeargument setting. For the proof of the global estimate, we have applied thereflection and approximation techniques.

Calder\'on-Zygmund type estimate for the parabolic double-phase system