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2015•Canadian Journal of MathematicsOpen access

On the Commutators of Singular Integral Operators with Rough Convolution Kernels

Guo Xiao-li, Guoen Hu

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Abstract

Abstract Let TΩ be the singular integral operator with kernel , where Ω is homogeneous of degree zero, has mean value zero, and belongs to Lq(Sn–1) for some q ∊ (1,∞). In this paper, the authors establish the compactness on weighted Lp spaces and the Morrey spaces, for the commutator generated by CMO(ℝn) function and TΩ. The associated maximal operator and the discrete maximal operator are also considered.

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Abstract Let TΩ be the singular integral operator with kernel , where Ω is homogeneous of degree zero, has mean value zero, and belongs to Lq(Sn–1) for some q ∊ (1,∞). In this paper, the authors establish the compactness on weighted Lp spaces and the Morrey spaces, for the commutator generated by CMO(ℝn) function and TΩ. The associated maximal operator and the discrete maximal operator are also considered.

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Available abstract

Abstract Let TΩ be the singular integral operator with kernel , where Ω is homogeneous of degree zero, has mean value zero, and belongs to Lq(Sn–1) for some q ∊ (1,∞). In this paper, the authors establish the compactness on weighted Lp spaces and the Morrey spaces, for the commutator generated by CMO(ℝn) function and TΩ. The associated maximal operator and the discrete maximal operator are also considered.

Key concepts: Mathematics, Commutator, Singular integral, Kernel (algebra), Pure mathematics, Operator (biology), Zero (linguistics), Convolution (computer science)

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