1. Boundedness and compactness of commutators associated with Lipschitz functions.
- Author
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Guo, Weichao, He, Jianxun, Wu, Huoxiong, and Yang, Dongyong
- Subjects
- *
COMMUTATORS (Operator theory) , *COMMUTATION (Electricity) , *SINGULAR integrals , *FRACTIONAL integrals , *INTEGRAL operators , *FUNCTION spaces - Abstract
Let α ∈ (0 , 1 ] , β ∈ [ 0 , n) and T Ω , β be a singular or fractional integral operator with homogeneous kernel Ω. In this paper, a CMO type space CMO α (ℝ n) is introduced and studied. In particular, the relationship between CMO α (ℝ n) and the Lipchitz space Lip α (ℝ n) is discussed. Moreover, a necessary condition of restricted boundedness of the iterated commutator (T Ω , β) b m on weighted Lebesgue spaces via functions in L i p α (ℝ n) , and an equivalent characterization of the compactness for (T Ω , β) b m via functions in CMO α (ℝ n) are obtained. Some results are new even in the unweighted setting for the first-order commutators. [ABSTRACT FROM AUTHOR]
- Published
- 2022
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