LAUSR

We study the Cauchy problem for Hartree equation with cubic convolution nonlinearity $$F(u) = (K \star |u|^{2k})u$$F(u)=(K⋆|u|2k)u under a specified condition on potential K with Cauchy data in modulation spaces $$M^{p,q}(\mathbb {R}^n)$$Mp,q(Rn). We establish global well-posedness results in $$M^{1,1}(\mathbb {R}^n)$$M1,1(Rn), when $$K(x)= \frac{\lambda }{|x|^{\nu }} ~ (\lambda \in \mathbb {R}, ~ 0< \nu < min\{2, \frac{n}{2}\})$$K(x)=λ|x|ν(λ∈R,0<ν