## A note on twisted discrete singular Radon transforms

In this paper we consider three types of discrete operators stemming from singular Radon transforms. We first extend an ℓp 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. Second, we note an ℓ2 bound for quasi-translation invariant discrete twisted Radon transforms. Finally, we extend an existing ℓ2 bound for a closely related non-translation invariant discrete oscillatory integral operator with singular kernel to an ℓp bound for all 1 < p < 1∞. 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. Copyright © 2010 International Press.

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- General Mathematics
- 4904 Pure mathematics
- 0101 Pure Mathematics

### Citation

*Mathematical Research Letters*,

*17*(4), 701–720.

*Mathematical Research Letters*17, no. 4 (2010): 701–20.

*Mathematical Research Letters*, vol. 17, no. 4, 2010, pp. 701–20.

## Published In

## ISSN

## Publication Date

## Volume

## Issue

## Start / End Page

## Related Subject Headings

- General Mathematics
- 4904 Pure mathematics
- 0101 Pure Mathematics