On Vinogradov's estimate of trigonometric sums and the Goldbach-Vinogradov theorem
Error Estimates in Renewal Theory
Dilations associated to flat curves.
I would like to give an exposition of the recent work of Tony Carbery, Mike Christ, Jim Vance, David Watson and myself concerning Hilbert transforms and Maximal functions along curves in R [CCVWW].
An asymptotic series expansion of the multidimensional renewal measure
The estimation of an integral arising in multiplier transformations
Singular Radon transforms and maximal functions under convexity assumptions.
We prove variable coefficient analogues of results in [5] on Hilbert transforms and maximal functions along convex curves in the plane.
The Hilbert transform and maximal function along nonconvex curves in the plane.
In this paper we study the Hilbert transform and maximal function related to a curve in R.
Singular integrals and the Newton diagram.
We examine several scalar oscillatory singular integrals involving a real-analytic phase function φ(s,t) of two real variables and illustrate how one can use the Newton diagram of φ to efficiently analyse these objects. We use these results to bound certain singular integral operators.
Discrete analogues of singular and maximal Radon transforms.
Singular and maximal Radon transforms: Analysis and geometry.
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