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We study the dispersion-generalized Benjamin-Ono equation in the periodicsetting. This equation interpolates between the Benjamin-Ono equation($\alpha=1$) and the viscous Burgers' equation ($\alpha=0$). We obtain localwell-posedness in $H^s$ for $s>3/2-\alpha$ and $\alpha\in(0,1)$ by using theshort-time Fourier restriction method.

Well-posedness of the periodic dispersion-generalized Benjamin-Ono equation in the weakly dispersive regime