A note on twisted discrete singular Radon transforms
- Autores: Lillian B. Pierce
- Localización: Mathematical research letters, ISSN 1073-2780, Vol. 17, Nº 4, 2010, págs. 701-720
- Idioma: inglés
- DOI: 10.4310/mrl.2010.v17.n4.a10
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Resumen
In this paper we consider three types of discrete operators stemming from singular Radon transforms. We first extend 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. Second, we note an $\ell^2$ bound for quasi-translation invariant discrete twisted Radon transforms. Finally, we extend 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.
