Weighted estimates for rough oscillatory singular integrals

Harri Ojanen
February 1999

Abstract: Weighted tex2html_wrap_inline58 estimates ( tex2html_wrap_inline60 ) are shown for oscillatory singular integral operators with polynomial phase and a rough kernel of the form tex2html_wrap_inline62 . We assume that tex2html_wrap_inline64 is homogeneous of degree zero and tex2html_wrap_inline66 . The radial factor h has bounded variation. The necessary condition on the weight is similar to the tex2html_wrap_inline70  condition but involves rectangles (instead of cubes) arising from a covering of a star-shaped set related to  tex2html_wrap_inline72 .

Keywords: oscillatory singular integral, rough kernel, weighted estimate, star-shaped set

AMS Mathematics Subject Classification: Primary 42B20

Journal of Fourier Analysis and Applications, vol. 6, 2000.

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