Potential Analysis

, Volume 42, Issue 3, pp 717–748 | Cite as

Boundedness and Compactness for the Commutators of Bilinear Operators on Morrey Spaces



Denote by T and \(\mathcal {I}_{\alpha }\) the bilinear Calderón-Zygmund operator and bilinear fractional integrals, respectively. In this paper we give the boundedness and compactness of the commutators [T,b] i , maximal operator T ∗,b,i and \([\mathcal {I}_{\alpha },b]_{i}\) on Morrey spaces. More precisely, we prove that [T,b] i , T ∗,b,i and \([\mathcal {I}_{\alpha },b]_{i}\) are all the bounded operators (if bB M O) and compact operators (if bC M O, the BMO-closure of \(C_{c}^{\infty }\)) from \(L^{p_{1},\lambda _{1}}\times L^{p_{2},\lambda _{2}}\) to L p, λ for some suitable indexes λ, λ 1, λ 2 and p, p 1, p 2. As an application of our results, we give also the boundedness and compactness of the commutators formed by the bilinear pseudodifferential operators on Morrey spaces.


Bilinear Calderón-Zygmund operator Bilinear maximal operator Bilinear fractional integral Commutator CMO space Compactness Morrey space 

Mathematics Subject Classifications (2010)

Primary 42B20, 42B25 Secondary 42B99 


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© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.School of Mathematical SciencesBeijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of EducationBeijingPeople’s Republic of China

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