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In this work we prove that the initial value problem (IVP) associated to thetwo-dimensional Benjamin-Ono equation $$\left. \begin{array}{rl} u_t+\mathcal H\Delta u +uu_x &\hspace{-2mm}=0,\qquad\qquad (x,y)\in\mathbb T^2,\; t\in\mathbbR,\\ u(x,y,0)&\hspace{-2mm}=u_0(x,y), \end{array} \right\}\,,$$ where $\mathcalH$ denotes the Hilbert transform with respect to the variable $x$ and $\Delta$is the Laplacian with respect to the spatial variables $x$ and $y$, is locallywell-posed in the periodic Sobolev space $H^s(\mathbb T^2)$, with $s>7/4$.

Periodic Cauchy Problem for one Two-dimensional Generalization of the Benjamin-Ono Equation in Sobolev Spaces of Low Regularity