Weighted estimates for rough oscillatory singular integrals |
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Authors: | Harri Ojanen |
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Institution: | (1) MathEngine Oy, Melkonkatu 18A, 00120 Helsinki, Finland |
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Abstract: | Weighted Lp estimates (1<p<∞) are shown for oscillatory singular integral operators with polynomial phase and a rough kernel of the form
eiP(x,y)Ω(x−y)h(|x−y|)|x−y|−n. We assume that Ω∈L logL(Sn−1) is homogeneous of degree zero and ∫Sn-1Ω=0. The radial factor h has bounded variation. The necessary condition on the weight is similar to the Ap condition but involves rectangles (instead of cubes) arising from a covering of a star-shaped set related to Ω. |
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Keywords: | 42B20 |
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