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LetTΩ,α (0 ≤ α< n) be the singular and fractional integrals with variable kernel Ω(x, z), and [b, TΩ,α] be the commutator generated by TΩ,α and a Lipschitz functionb. In this paper, the authors study the boundedness of [b, TΩ,α] on the Hardy spaces, under some assumptions such as theLr-Dini condition. Similar results and the weak type estimates at the end-point cases are also given for the homogeneous convolution operators$$T_{\tilde \Omega ,\alpha } (0 \leqslant \alpha< n)$$. The smoothness conditions imposed on$$\tilde \Omega $$ are weaker than the corresponding known results.
Volume 132, 2022
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