Аннотация:Consider a parabolic N×N-system of order m on ℝn with top-order coefficients aα VMO∩L∞. Let 1 < p, q < ∞ and let ω be a Muckenhoupt weight. It is proved that systems of this kind possess a unique solution u satisfying ∥ u ′ ∥ L q ( J ; L ω p ( ℝ n ) N ) + ∥ A u ∥ L q ( J ; L ω p ( ℝ n ) N ) ⩽ C ∥ f ∥ L q ( J ; L ω p ( ℝ n ) N ) , where Au = ∑|α|⩽m aα Dαu and J = [0,∞). In particular, choosing ω = 1, the realization of A in Lp(ℝn)N has maximal Lp – Lq regularity.
