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Integral inequalities for the Hilbert transform applied to a nonlocal transport equation

Authors:	Antonio Crdoba Diego Crdoba Marco A Fontelos

Institution:	^aDepartamento de Matemáticas, Universidad Autónoma de Madrid, 28049 Madrid, Spain;^bInstituto de Matemáticas y Física Fundamental, Consejo Superior de Investigaciones Científicas, C/Serrano 123, Madrid 28006, Spain

Abstract:	We prove several weighted inequalities involving the Hilbert transform of a function f(x) and its derivative. One of those inequalities, is used to show finite time blow-up for a transport equation with nonlocal velocity.

Keywords:	Integral inequalities Hilbert transform Transport equations
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