Strongly singular integral operators satisfy weighted L^∞-BMO boundedness for Muckenhoupt weights, generalizing Miyachi, and this yields an alternative proof of Chanillo's weighted L^p estimates via extrapolation.
Fefferman,Inequalities for strongly singular convolution operators, Acta Math.124(1970), 9–36
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Continuity properties of strongly singular integral operators for extreme values of $p$
Strongly singular integral operators satisfy weighted L^∞-BMO boundedness for Muckenhoupt weights, generalizing Miyachi, and this yields an alternative proof of Chanillo's weighted L^p estimates via extrapolation.