Boundedness for multilinear commutator of Marcinkiewicz operator with variable kernels on Hardy and Herz-Hardy spaces

Wenxin Yu,Yigang He,Xianming Wu,Qiwu Luo,Jian Zheng

doi:10.1186/1029-242x-2012-308

Wenxin Yu, Yigang He + Show 3 more

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https://doi.org/10.1186/1029-242x-2012-308

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Abstract

In this paper, the - and -type boundedness for the multilinear commutator related to the Marcinkiewicz operator with variable kernels is obtained. MSC:42B20, 42B25.

Highlights

Introduction and definitions LetT be the Calderón-Zygmund operator and b ∈ BMO(Rn)
2 Theorems and proofs We begin with three preliminary lemmas
Proof It suffices to show that there exists a constant C > such that for every (p, b) atom a, μb(a) Lq ≤ C

Summary

Introduction

Introduction and definitions LetT be the Calderón-Zygmund operator and b ∈ BMO(Rn). The commutator [b, T] generated by T and b is defined by [b, T](f )(x) = b(x)T(f )(x) – T(bf )(x).A classical result of Coifman, Rochberg and Weiss (see [ , ]) proved that the commutator [b, T] is bounded on Lp(Rn) ( < p < ∞). A bounded measurable function a on Rn is said to be a (p, b) atom if Given a set E ⊂ Rn, the characteristic function of E is defined by χE. Definition Let < p, q < ∞, α ∈ R.

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Conclusion