• Commutators of integral operators with variable kernels on Hardy spaces

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      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< 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.

    • Author Affiliations

       

      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
    • Dates

       
  • Proceedings – Mathematical Sciences | News

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