Discrete fractional Radon transforms and quadratic forms
نویسندگان
چکیده
منابع مشابه
Discrete Fractional Radon Transforms and Quadratic Forms
We consider discrete analogues of fractional Radon transforms involving integration over paraboloids defined by positive definite quadratic forms. We prove that such discrete operators extend to bounded operators from `p to `q for a certain family of kernels. The method involves an intricate spectral decomposition according to major and minor arcs, motivated by ideas from the circle method of H...
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Received by the editors February 27, 2004. 1991 Mathematics Subject Classification. Primary 11L07, 42B20.
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The purpose of this paper is to describe recent results we have obtained in finding discrete analogues of the theory of singular integrals on curves, or more generally of "singular Radon transforms," at least in the translation-invariant case. Our theorems are related to estimates for certain exponential sums that arise in number theory; they are also connected with Bourgain's recent maximal er...
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ژورنال
عنوان ژورنال: Duke Mathematical Journal
سال: 2012
ISSN: 0012-7094
DOI: 10.1215/00127094-1507288