We establish Littlewood–Paley decompositions for Muckenhoupt weights in the setting of UMD spaces. As a consequence we obtain two-weight variants of the Mikhlin multiplier theorem for operator-valued multipliers. We also show two-weight estimates for multipliers satisfying Hörmander type conditions.

中文翻译：

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运算符值傅立叶乘法器的加权估计

我们在UMD空间的环境中为Muckenhoupt权重建立Littlewood-Paley分解。结果，我们为算子值乘子获得了米克林乘子定理的两个权重变体。我们还显示了满足荷曼德类型条件的乘数的两次加权估计。