A note on the Ostrovsky equation in weighted Sobolev spaces

In this work we consider the initial value problem (IVP) associated to the Ostrovsky equationsut+∂x3u±∂x−1u+u∂xu=0,x∈R,t∈R,u(x,0)=u0(x).} We study the well-posedness of the IVP in the weighted Sobolev spacesZ˙s,s2:={f∈Hs(R):∂x−1f∈L2(R)}∩L2(|x|sdx), with 34