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https://www.ias.ac.in/article/fulltext/pmsc/115/04/0399-0410

Singular and fractional integrals; variable kernel; commutator; Hardy space

LetT_Ω,α (0 ≤ α< n) be the singular and fractional integrals with variable kernel Ω(x, z), and [b, T_Ω,α] be the commutator generated by T_Ω,α and a Lipschitz functionb. In this paper, the authors study the boundedness of [b, T_Ω,α] on the Hardy spaces, under some assumptions such as theL^r-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.

Pu Zhang¹ Kai Zhao²

1. Institute of Mathematics, Zhejiang Sci-Tech University, Hangzhou - 310018, People’s Republic of China
2. Department of Mathematics, Qingdao University, Qingdao - 266071, People’s Republic of China

Manuscript received

26 January 2005

Manuscript revised

13 July 2005