On Wiener’s Tauberian theorems and convolution for oscillatory integral operators

Tauberian theorems for sum sets

Introduction. The sums formed from the set of non-negative powers of 2 are just the non-negative integers. It is easy to obtain “abelian” results to the effect that if a set is distributed like the powers of 2, then the sum set will be distributed like Dhe non-negative integers. We will be concerned here with converse, or “Tauberian” results. The main theme of this paper is t’he following quest...

Tauberian Theorems for Summability Transforms

we then write sn → s(A), where A is the A method of summability. Appropriate choices of A= [an,k] for n,k ≥ 0 give the classical methods [2]. In this paper, we present various summability analogs of the strong law of large numbers (SLLN) and their rates of convergence in an unified setting, beyond the class of random-walk methods. A convolution summability method introduced in the next section ...

A Note on Calderón-zygmund Singular Integral Convolution Operators

Oscillatory Integral Operators with Low–order Degeneracies

We prove sharp L estimates for oscillatory integral and Fourier integral operators for which the associated canonical relation C ⊂ T ∗ΩL × T ∗ΩR projects to T ∗ΩL and to T ∗ΩR with corank one singularities of type ≤ 2. This includes two-sided cusp singularities. Applications are given to operators with one-sided swallowtail singularities such as restricted X-ray transforms for well-curved line ...

On Oscillatory Integral Operators with Folding Canonical Relations

1.Introduction Let X and Y be open sets in R d and let X Y be a bounded open set whose closure is contained in X Y. We consider oscillatory integral operators Here 1 and is a parameter in a manifold ?. We assume that a ;; 2 C 1 0 (() It may sometimes be convenient to admit some growth in for the (x; y) derivatives of the amplitude. Let 0 1. We shall say that the family of amplitudes