|Revista Colombiana de Matemáticas|
Abstract. In this article we obtain estimates of Strichartz type, of maximal type, and of local type for the linearized KPI and KPII equations. These estimates show the gain of regularity of the solutions of these equations and are obtained by a detailed analysis of the oscillatory integrals wich give the solutions explicitly.Palabras claves. Kadomtsev - Petviashvili equation, smoothing effects, dispersive equations.