• Commutators of integral operators with variable kernels on Hardy spaces

• # Fulltext

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

• # Keywords

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

• # Abstract

LetTΩ,α (0 ≤ α&lt; 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$$T_{\tilde \Omega ,\alpha } (0 \leqslant \alpha&lt; n)$$. The smoothness conditions imposed on$$\tilde \Omega$$ are weaker than the corresponding known results.

• # Author Affiliations

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

• # Proceedings – Mathematical Sciences

Volume 130, 2020
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Continuous Article Publishing mode

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019