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

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5 papers · 1 filter

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…

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.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…