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# Certain Operators with Rough Singular Kernels

Published:2003-06-01
Printed: Jun 2003
• Jiecheng Chen
• Dashan Fan
• Yiming Ying
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## Abstract

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 - Singular and oscillatory integrals (Calderon-Zygmund, etc.) 42B25 - Maximal functions, Littlewood-Paley theory 42B15 - Multipliers