David J. Rule

activity

20112026

most citedThe Integrability of Negative Powers of the Solution of the Saint Venant Problem

4 citations · 7 across the 10 of their papers we have counts for

collaborators

11 papers

math.CA2026

Rubio de Francia's Extrapolation Theorem and Sparse Bounds

David Rule

Sparse bounds have proved to be a powerful tool which simplify the understanding of many important operators in harmonic analysis. The existence of a sparse bound for an operator i…

math.CA2026

Sparse Bounds for Rough Fourier Integral Operators

Wellars Banzi, Froduald Minani, Solange Mukeshimana +1

We prove pointwise bounds for rough Fourier integral operators by the $L^{p}$ Hardy-Littlewood maximal function. We assume the Fourier integral operators have amplitudes in $L^\infty…

math.AP2023

Multilinear oscillatory integrals and estimates for coupled systems of dispersive PDEs

Aksel Bergfeldt, Salvador Rodriguez-Lopez, David Rule +1

We establish sharp global regularity of a class of multilinear oscillatory integral operators that are associated to nonlinear dispersive equations with both Banach and quasi-Banac…

q-bio.TO2017★ 1 cited

A two dimensional model of curvilinear blood vessels with layered elastic walls

Arpan Ghosh, Vladimir Kozlov, Sergey Nazarov +1

We present a two dimensional model describing the elastic behaviour of the wall of a curved blood vessel. The wall has a laminate structure consisting of several anisotropic layers…

math.AP2014

A Seeger-Sogge-Stein theorem for bilinear Fourier integral operators

Salvador Rodríguez-López, David Rule, Wolfgang Staubach

We establish the regularity of bilinear Fourier integral operators with bilinear amplitudes in $S_{1, 0}^{m} (n, 2)$ and non-degenerate phase functions, from $L^{p} \times L^{q} \to L^{r}$ u…

math.CA2013

Boundary value problems for degenerate elliptic equations and systems

Pascal Auscher, Andreas Rosén, David Rule

We study boundary value problems for degenerate elliptic equations and systems with square integrable boundary data. We can allow for degeneracies in the form of an $A_{2}$ weight.…

math.CA2012★ 1 cited

Multilinear pseudodifferential operators beyond Calderón-Zygmund theory

Nicholas Michalowski, David J. Rule, Wolfgang Staubach

We consider two types of multilinear pseudodifferential operators. First, we prove the boundedness of multilinear pseudodifferential operators with symbols which are only measurabl…

math.AP2012★ 4 cited

The Integrability of Negative Powers of the Solution of the Saint Venant Problem

Anthony Carbery, Vladimir Maz'ya, Marius Mitrea +1

We initiate the study of the finiteness condition $\int_{Ω} u (x)^{- β} d x \leq C (Ω, β) < + \infty$ where $Ω \subseteq R^{n}$ is an open set and $u$ is the solution of the Saint Vena…

math.AP2011★ 1 cited

Global boundedness of multilinear Fourier integral operators

Salvador Rodriguez-Lopez, Wolfgang Staubach

We study the global boundedness of bilinear and multilinear Fourier integral operators on Banach and quasi-Banach $L^{p}$ spaces, where the amplitudes of the operators are smooth or…

math.AP2011

On the boundedness of certain bilinear Fourier integral operators

Salvador Rodriguez-Lopez, David J. Rule, Wolfgang Staubach

We prove the global $L^{2} \times L^{2} \to L^{1}$ boundedness of bilinear Fourier integral operators with amplitudes in $S_{1, 0}^{0} (n, 2)$ . To achieve this, we require that the phase fun…

math.SP2011

On the stability of a forward-backward heat equation

Lyonell Boulton, Marco Marletta, David Rule

In this paper we examine spectral properties of a family of periodic singular Sturm-Liouville problems which are highly non-self-adjoint but have purely real spectrum. The problem…