V,M为函数空间,M L^p(R^d).对ε∈∧,Tε:V→M为一个线性算子.N:R^d→∧以为有限值函数.说明了当∧=N或诸Tε都下半连续时,诸TN的一致弱(或强)有界性蕴含极大算子的相应有界性.
Let V,M be function spaces and M L^P(R^d). For ε∈∧, let Tε :V→M be a linear operator. Let N: R^d→∧ be a function with finite range. In this paper the uniform weak (or strong) boundedness of TN's that implies the corresponding boundedness of maximal operator when ∧ = N or Tε's are lower semicontinuous is shown.