Displaying similar documents to “An extension of Bourgain and Garaev's sum-product estimates”

Resolvent estimates with mild trapping

Jared Wunsch (2012)

Journées Équations aux dérivées partielles

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We discuss recent progress in understanding the effects of certain trapping geometries on cut-off resolvent estimates, and thus on the qualititative behavior of linear evolution equations. We focus on trapping that is unstable, so that strong resolvent estimates hold on the real axis, and large resonance-free regions can be shown to exist beyond it.

Estimates for the arctangent function related to Shafer's inequality

Cristinel Mortici, H. M. Srivastava (2014)

Colloquium Mathematicae

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The aim of this article is to give new refinements and sharpenings of Shafer's inequality involving the arctangent function. These are obtained by means of a change of variables, which makes the computations much easier than the classical approach.

The FBI transform, operators with nonsmooth coefficients and the nonlinear wave equation

Daniel Tataru (1999)

Journées équations aux dérivées partielles

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The aim of this work is threefold. First we set up a calculus for partial differential operators with nonsmooth coefficients which is based on the FBI (Fourier-Bros-Iagolnitzer) transform. Then, using this calculus, we prove a weaker version of the Strichartz estimates for second order hyperbolic equations with nonsmooth coefficients. Finally, we apply these new Strichartz estimates to second order nonlinear hyperbolic equations and improve the local theory, i.e. prove local well-posedness...