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

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On a transport equation with nonlocal drift (2014, methodology): “This blowup proof was extended in [17] to cover a much wider class of initial data, via a series of new weighted integral inequalities (which are interesting in their own right).”
On the Loss of Continuity for Super-Critical Drift-Diffusion Equations (2012, methodology): “For example, this is the case in Burgers equation with fractional diffusion [1, 26], the Keller-Segel model [21], and many other equations [12, 17, 29].”
Well-posedness for a transport equation with nonlocal velocity (2008, unknown): “5 (Córdoba, Córdoba and Fontelo [4], [5]).”