Related papers: Multilinear Oscillatory Integrals Via Reduction of…
We use tools from the multilinear oscillatory integral program developed by Christ, Li, Thiele, and Tao to treat special cases which are not covered by existing theory. Consideration of special cases leads to an extended class of examples…
In this article we prove a sharp decay estimate for certain multilinear oscillatory integral operators of a form inspired by the general framework of Christ, Li, Tao, and Thiele [6]. A key purpose of this work is to determine when such…
In 2005, Li, Tao, Thiele and the author raised a general question concerning upper bounds for a class of multilinear oscillatory integral operators, and established such bounds in a few cases. Most cases remain open. The present paper is…
We apply the Bennett-Carbery-Tao multilinear restriction estimate in order to bound restriction operators and more general oscillatory integral operators. We get improved L^p estimates in the Stein restriction problem for dimension at least…
In this paper, the boundedness properties for some multilinear operators related to certain integral operators from Lebesgue spaces to Orlicz spaces are obtained. The operators include Calder\'on--Zygmund singular integral operator,…
Basic questions concerning nonsingular multilinear operators with oscillatory factors are posed and partially answered. Lebesgue space norm inequalities are established for multilinear integral operators of Calderon-Zygmund type which…
In this paper we prove sharp $L^\infty$-$L^\infty$-$L^\infty$ decay for certain trilinear oscillatory integral forms of convolution type on $\mathbb R^2$. These estimates imply earlier $L^2$-$L^2$-$L^2$ results obtained by the second author…
The aim of this paper is to prove the boundedness of the oscillation and variation operators for the multilinear singular integrals with Lipschitz functions on weighted Morrey spaces.
We mostly survey results concerning the $L^2$ boundedness of oscillatory and Fourier integral operators. This article does not intend to give a broad overview; it mainly focusses on a few topics directly related to the work of the authors.
We obtain two-weighted $L^2$ norm inequalities for oscillatory integral operators of convolution type on the line whose phases are of finite type. The conditions imposed on the weights involve geometrically-defined maximal functions, and…
Inequalities are established for certain trilinear scalar-valued functionals. These functionals act on measurable functions of one real variable, are defined by integration over two- or three-dimensional spaces, and are controlled in terms…
In this paper, two multiscale time integrators (MTIs), motivated from two types of multiscale decomposition by either frequency or frequency and amplitude, are proposed and analyzed for solving highly oscillatory second order differential…
We examine a certain class of trilinear integral operators which incorporate oscillatory factors e^{iP}, where P is a real-valued polynomial, and prove smallness of such integrals in the presence of rapid oscillations.
The purpose of this paper is to establish the weighted norm inequalities of one-sided oscillatory integral operators by the aid of interpolation of operators with change of measures.
In this paper, we establish the global boundedness of oscillatory integral operators on Besov-Lipschitz and Triebel-Lizorkin spaces, with amplitudes in general $S^m_{\rho,\delta}(\mathbb{R}^n)$-classes and non-degenerate phase functions in…
In this paper, the main purpose is to consider a number of results concerning boundedness of multilinear fractional Calder\'{o}n-Zygmund operators with kernels of mild regularity. Let $T_{\alpha}$ be a multilinear fractional…
This paper investigates a class of non-autonomous highly oscillatory ordinary differential equations characterized by a linear component inversely proportional to a small parameter $\varepsilon$, with purely imaginary eigenvalues, and an…
In this paper, we will present a generalization for a minimization problem from I. Daubechies, M. Defrise, and C. Demol [3]. This generalization is useful for solving many practical problems in which more than one constraint are involved.…
In the paper we prove several inequalities involving two isotonic linear functionals. We consider inequalities for functions with variable bounds, for Lipschitz and H\" older type functions etc. These results give us an elegant method for…
We prove a weak-type estimate for a class of operators extending some of the almost orthogonality issues involved in the study of the bilinear Hilbert transform by Lacey and Thiele.