Martingale square functions with matrix weights satisfy L_p bounds characterized by matrix A_p conditions, with sharpness for 1<p≤2 and optimal exponents achieved in the scalar case for all 1<p<∞.
Volberg,MatrixA p weights viaS-functions, J
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Sharp weighted norm estimates for martingale square functions
Martingale square functions with matrix weights satisfy L_p bounds characterized by matrix A_p conditions, with sharpness for 1<p≤2 and optimal exponents achieved in the scalar case for all 1<p<∞.