弱Hardy空间上的参数型Marcinkiewicz积分

摘要

证明了参数型Marcinkiewicz积分μΝΩ是(Hp,∞,Lp,∞)(0＜p≤1)型的算子,这里Ω是满足Lipα条件的Rn上的零次齐次函数.对于p=1,减弱了Ω的条件仍得到μpΩ是(H1,∞,L1,∞)型的.作为上述结果的推论,得到了μρΩ是弱(1,1)型的算子.%we prove that the parametric Marcinkiewicz integralμρΩis an operator of type (Hp,∞,Lp,∞)(0＜p≤1),if Ω∈Lipα is a homogeneous function of degree zero.For p=1,we weaken the smoothness condition assumed on Ω and again obtain μρΩ is of type (H1,∞,L1,∞).As a corollary of the results above,we give the weak type(1,1) boundedness of μpΝΩ.