Commutators of Integral Operators with Variable Kernels on Hardy Spaces

[摘要] Let $T_{𝛺,𝛼}(0≤𝛼 < n)$ 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 function 𝑏. In this paper, the authors study the boundedness of $[b, T_{𝛺,𝛼}]$ on the Hardy spaces, under some assumptions such as the $L^r$-Dini condition. Similar results and the weak type estimates at the end-point cases are also given for the homogeneous convolution operators $T_{overline{𝛺},𝛼}(0≤𝛼 < n)$. The smoothness conditions imposed on $overline{𝛺}$ are weaker than the corresponding known results.

[学科分类] 数学（综合）

[关键词] Singular and fractional integrals;variable kernel;commutator;Hardy space.