Well-posed solutions of the third order Benjamin-Ono equation in weighted Sobolev spaces

Here we continue the study of the initial value problem for the third order Benjamin-Ono equation in the weighted Sobolev spaces H-gamma(s) = H-s boolean AND L-gamma 2, where s > 3, gamma greater than or equal to 0. The result is the proof of well-posedness of the afore mentioned problem in H-gamma(s), s > 3, gamma is an element of [0, 1]. The proof involves the use of parabolic regularization, the Riesz-Thorin interpolation theorem and the construction technique of auxiliary functions.