Continuity properties for commutators of multilinear type operators on product of certain Hardy spaces |
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Authors: | Wenjuan Li Qingying Xue |
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Affiliation: | School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, China |
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Abstract: | Similar to the property of a linear Calderón-Zygmund operator, a linear fractional type operator Iα associated with a BMO function b fails to satisfy the continuity from the Hardy space Hp into Lp for p≤1. Thus, an alternative result was given by Y. Ding, S. Lu and P. Zhang, they proved that [b, Iα] is continuous from an atomic Hardy space Hbp into Lp,where Hbp is a subspace of the Hardy space Hp for n/(n+1)<p≤1. In this paper, we study the commutators of multilinear fractional type operators on product of certain Hardy spaces. The endpoint (Hb1p1×?×Hbmpm, Lp) boundedness for multilinear fractional type operators is obtained. We also give the boundedness for the commutators of multilinear Calderón-Zygmund operators and multilinear fractional type operators on product of certain Hardy spaces when b∈(Lipβ)m(?n). |
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Keywords: | Multilinear fractional type operator multilinar Calderdn-Zygmundoperator commutator Hardy type space |
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