可变核Marcinkiewicz积分交换子在Herz型Hardy空间上的有界性

Abstract

Abstract:

The authors of this article are interested in the commutator μ_Ω_{, b} generated by a function b ∈Lip_β(Rⁿ)(0 < β ≤ 1) and the Marcinkiewicz integrals μ_Ωwith variable kernel Ω ∈L^∞(Rⁿ) ×L^r(S^n-1) (r ≥ 1). The boundedness results forμ_Ω, _b in the homogeneous Herz-type Hardy spaces are obtained. Moreover, The same results are shown for the commutator μ^ρ_{Ω, b} related to the parametric Marcinkiewicz integral μ^ρ_Ω.

Key words: Commutator, Marcinkiewicz integral with variable kernel, Herz-type Hardy space, L^r, γ-Dini condition, Lip_β function

CLC Number:

42B20

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TAO Xiang-Xin, WEI Rui-Ying. Boundedness of Commutators Related to Marcinkiewicz Integrals with Variable Kernels in Herz-type Hardy Spaces[J].Acta mathematica scientia,Series A, 2009, 29(6): 1508-1517.

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Boundedness of Commutators Related to Marcinkiewicz Integrals with Variable Kernels in Herz-type Hardy Spaces

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