On multilinear commutators of Θ-type Calderón-Zygmund operators

Xie, Rulong; Li-sheng, Shu

doi:10.1007/s10496-008-0260-8

Cited by 7 publications

(2 citation statements)

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“…Given a locally integrable function b, the commutator generated by T θ and b is de ned by Such type of operators are extensively applied in PDE with non-smooth area. Many authors concentrate on the boundedness of these operators on various function spaces, we refer the reader to see [8][9][10][11][12][13][14] for its developments and applications. In [11], Quek-Yang established the boundedness of T θ on spaces such as weighted Lebesgue spaces, weighted weak Lebesgue spaces, weighted Hardy spaces and weighted weak Hardy spaces.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

θ-type Calderón-Zygmund Operators and Commutators in Variable Exponents Herz space

Yang

Tao

2018

Open Mathematics

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The aim of this paper is to deal with the boundedness of the θ-type Calderón-Zygmund operators and their commutators on Herz spaces with two variable exponents p(⋅), q(⋅). It is proved that the θ-type Calderón-Zygmund operators are bounded on the homogeneous Herz space with variable exponents $\begin{array}{} \displaystyle \dot{K}^{\alpha,q(\cdot)}_{p(\cdot)}(\mathbb{R}^{n}). \end{array}$ Furthermore, the boundedness of the corresponding commutators generated by BMO function and Lipschitz function is also obtained respectively.

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