Contractive multipliers from Hardy space to weighted Hardy space
  It is shown how any contractive multiplier from the Hardy space to a weighted Hardy space $H^{2}_{\bbeta}$ can be factored as a fixed factor composed with the classical Schur multiplier (contractive multiplier between Hardy spaces). The result is applied to get results on interpolation for a Hardy-to-weighted-Hardy contractive multiplier class. 
Joseph A. Ball and Vladimir Bolotnikov
math.CA math.FA