The existence and boundedness of multilinear Marcinkiewicz integrals on Companato spaces

الأصل · EN

In this paper, we established the boundedness of m-linear Marcinkiewicz integral on Campanato type spaces. We showed that if the m-linear Marcinkiewicz integral is finite for one point, then it is finite almost everywhere. Moreover, the following norm inequality holds, μ(f)ₑα,ᵖ ≤ C∏ⱼ₌₁ᵐfⱼₑαʲ,ᵖʲ, where Eα,ᵖ is the classical Campanato spaces.