A note on twisted discrete singular Radon transforms
The author considers three types of discrete operators stemming from singular Radon transforms. She first extends an \(\ell^p\) result for translation invariant discrete singular Radon transforms to a class of twisted operators including an additional oscillatory component, via a simple method of descent argument. We note an \(\ell^2\) bound for quasi-translation invariant discrete twisted Radon transforms. Finally, the author extends an existing \(\ell^2\) bound for a closely related non-translation invariant discrete oscillatory integral operator with singular kernel to an \(\ell^p\) bound for all \(1< p< \infty\). This requires an intricate induction argument involving layers of decompositions of the operator according to the Diophantine properties of the coefficients of its polynomial phase function.
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