<p>We study the <i>L</i><sup><i>p</i></sup> boundedness of singular integral operators along surfaces of revolution on product spaces. The <i>L</i><sup><i>p</i></sup> boundedness for these operators are obtained under very weak conditions on kernels. Our results are new and they improve several previously known results. Furthermore, they are natural extensions of many known results on singular integrals in the one-parameter setting and they subsume many other corresponding results on the product space setting.</p>

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Rough Singular Integrals Associated to Surfaces of Revolution on Product Spaces

  • Hussain Al-Qassem,
  • Leslie Cheng,
  • Yibiao Pan

摘要

We study the Lp boundedness of singular integral operators along surfaces of revolution on product spaces. The Lp boundedness for these operators are obtained under very weak conditions on kernels. Our results are new and they improve several previously known results. Furthermore, they are natural extensions of many known results on singular integrals in the one-parameter setting and they subsume many other corresponding results on the product space setting.