Interpolation of Matrix Weighted Spaces and Commutator Estimates
Abstract
We present a formula for the interpolation of matrix weighted spaces of vector valued functions via interpolation functors. We apply our formula to the particular case of interpolation of matrix weighted Lp spaces by the real and complex methods, and present consequences regarding the matrix Muckenhoupt classes and commutator estimates of Calder\'on-Zygmund operators with matrix BMO functions. In particular, we characterize the logarithms of Muckenhoupt weights through higher order commutators.
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