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Using a geometric method, we characterize all entire functions that transform the Bloch space into a Bergman space by superposition in terms of their order and type. We also prove that all superposition operators induced by such entire functions act boundedly. Similar results hold for superpositions from BMOA into Bergman spaces and from the Bloch space into certain weighted Hardy spaces.

We establish local higher integrability estimates for upper gradients of vector-valued parabolic quasi-minimizers in metric measure spaces, satisfying a doubling property and supporting a weak Poincaré inequality.

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