弱Hardy空间上的参数型Marcinkiewicz积分(英文)

Parametric Marcinkiewicz Integral on Weak Hardy Spaces

证明了参数型Marcinkiewicz积分μρΩ是(Hp,∞,Lp,∞)(0<p≤1)型的算子,这里Ω是满足Lipα条件的n上的零次齐次函数.对于p=1,减弱了Ω的条件仍得到μρΩ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 integral μΩ^p is an operator of type （H^p,∞ , L^p,∞ ） （0〈p≤1）, if Ω∈ Lip, is a homogeneous function of degree zero. For p= 1, we weaken the smoothness condition assumed on Ω and again obtain μΩ^p is of type （H^1,∞ ,L^1,∞ ）. As a corollary of the results above, we give the weak type （1,1） boundedness of μΩ^ρ.