A NOTE ON TWISTED DISCRETE SINGULAR RADON TRANSFORMS

作者：Pierce Lillian B^*

来源：Mathematical Research Letters, 2010, 17(4): 701-720.

In this paper we consider three types of discrete operators stemming from singular Radon transforms. We first extend an l(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 l(2) bound for quasi-translation invariant discrete twisted Radon transforms. Finally, we extend an existing l(2) bound for a closely related non-translation invariant discrete oscillatory integral operator with singular kernel to an l(p) bound for all 1 < p < infinity. 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.

• 出版日期2010-7