Rough singular integrals associated to polynomial curves
Rough singular integrals associated to polynomial curves
Abstract In this paper, the authors establish the boundedness of singular integral operators associated to polynomial curves as well as the related maximal operators with rough kernels $\Omega \in H^{1}({\mathrm{S}}^{n-1})$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Ω</mml:mi> <mml:mo>∈</mml:mo> <mml:msup> <mml:mi>H</mml:mi> <mml:mn>1</mml:mn> </mml:msup> <mml:mo>(</mml:mo> <mml:msup> <mml:mi>S</mml:mi> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> <mml:mo>)</mml:mo> </mml:math> and …