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<p>We study the singular integral operator along subspaces, which is a natural generalization of the directional singular integral operator. We show that singular integral operators along subspaces with standard kernels or rough kernels are bounded on mixed-norm Lebesgue spaces. Moreover, the operator norms are uniform with respect to the subspaces. As a consequence, we obtain the mixed-norm estimates for directional singular integral operators.</p>

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Mixed-Norm Estimates for Singular Integral Operators along Subspaces

  • 期刊论文

  • 发表日期：

    2026年5月11日

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  • Ting Chen,
  • Wenchang Sun

摘要

We study the singular integral operator along subspaces, which is a natural generalization of the directional singular integral operator. We show that singular integral operators along subspaces with standard kernels or rough kernels are bounded on mixed-norm Lebesgue spaces. Moreover, the operator norms are uniform with respect to the subspaces. As a consequence, we obtain the mixed-norm estimates for directional singular integral operators.