Continuity properties of strongly singular integral operators for extreme values of $p$
In this work, we establish continuity properties of strongly singular integral operators for extreme values of $p$. Particularly, weighted $L^\infty$-$BMO$ boundedness is obtained, generalizing Miyachi's result to the context of Muckenhoupt weights. As an application, we get an alternative proof of Chanillo's weighted $L^p$ estimates via extrapolation techniques.
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