Integral inequalities for the Hilbert transform applied to a nonlocal transport equation |
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Authors: | Antonio C rdoba, Diego C rdoba,Marco A. Fontelos |
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Affiliation: | 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 |
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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. |
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Keywords: | Integral inequalities Hilbert transform Transport equations |
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