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

该文研究由可变核Marcinkiewicz 积分和Lip_β (Rⁿ)(0 <β≤ 1)函数生成的交换子μ_{Ω, b}. 证明了当可变核Ω∈L^∞(Rⁿ)×L^r(S^n-1)(r≥1)$时, 交换子μ_{Ω, b}从Herz型Hardy空间到Herz空间的有界性. 同时建立了参数型Marcinkiewicz 积分的交换子μ^ρ_{Ω, b}在Herz型Hardy空间上的有界性.

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

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_Ω with variable kernel Ω ∈L^∞(Rⁿ) ×L^r(S^n-1) (r ≥ 1). The boundedness results for μ_{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.