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Certain Operators with Rough Singular Kernels

Open Access article
 Printed: Jun 2003
  • Jiecheng Chen
  • Dashan Fan
  • Yiming Ying
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We study the singular integral operator $$ T_{\Omega,\alpha}f(x) = \pv \int_{R^n} b(|y|) \Omega(y') |y|^{-n-\alpha} f(x-y)\,dy, $$ defined on all test functions $f$,where $b$ is a bounded function, $\alpha\geq 0$, $\Omega(y')$ is an integrable function on the unit sphere $S^{n-1}$ satisfying certain cancellation conditions. We prove that, for $1
MSC Classifications: 42B20, 42B25, 42B15 show english descriptions Singular and oscillatory integrals (Calderon-Zygmund, etc.)
Maximal functions, Littlewood-Paley theory
42B20 - Singular and oscillatory integrals (Calderon-Zygmund, etc.)
42B25 - Maximal functions, Littlewood-Paley theory
42B15 - Multipliers

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