Shu Li-sheng
Abstract
we prove that the parametric Marcinkiewicz integral μρΩ is an operator of type(Hp,∞,Lp,∞)(0p≤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 μρΩ.
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we prove that the parametric Marcinkiewicz integral μρΩ is an operator of type(Hp,∞,Lp,∞)(0p≤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 μρΩ.
Key concepts: Mathematics, Smoothness, Corollary, Type (biology), Parametric statistics, Mathematical analysis, Homogeneous, Operator (biology)