2012•Journal of Yantai UniversityRequires access

Boundedness of Commutators Related to Hyper-singular Marcinkiewicz Integral Commutator

Li Yin

Abstract

We study the boundedness of hyper-singular Marcinkiewicz integral μbΩ,ρ generated by function b∈Lipβ(Rn)(0β≤1) and a certain Marcinkiewicz integrals with variable kernel Ω(x,z)∈L∞(Rn)×Lr(Sn-1)(r2(n-1)/n) in the homogeneous Morrey-Herz spaces.Moreover,the same results are shown for the commutator μb,σΩ,ρ related to the parametric Marcinkiewicz integral.

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Key concepts: Commutator, Mathematics, Kernel (algebra), Homogeneous, Singular integral, Pure mathematics, Singular integral operators, Mathematical analysis