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Publications [#302451] of Lillian B. Pierce

Papers Published

  1. Pierce, LB, A note on twisted discrete singular Radon transforms, Mathematical Research Letters, vol. 17 no. 4 (2010), pp. 701-720, ISSN 1073-2780 [doi]
    (last updated on 2017/12/12)

    Abstract:
    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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