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Operators with rough singular kernels |
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| Authors: | Daning Chen Dashan Fan |
| Institution: | a Department of Mathematics, Jackson State University, Jackson, MS 39217, USA b School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China c Department of Mathematics, University of Wisconsin-Milwaukee, Milwaukee, WI 53201, USA d Central China Normal University, Wuhan 430074, China |
| Abstract: | For α>0, we study the singular integral operators TΩ,α and the Marcinkiewicz integral operator μΩ,α. The kernels of these operators behave like |y|−n−α near y=0, and contain a distribution Ω on the unit sphere Sn−1. We prove that if Ω∈Hr(Sn−1)(r=(n−1)/(n−1+α)) satisfying certain cancellation condition, then both TΩ,α and μΩ,α can be extend to be the bounded operators from the Sobolev space  to the Lebesgue space Lp(Rn). The result improves and extends some known results. |
| Keywords: | Singular integral Rough kernel Sobolev spaces Marcinkiewicz integral operator |
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