Global well-posedness for fractional Hartree equation on modulation spaces and Fourier algebra

We study the Cauchy problem for fractional Schrodinger equation with cubic convolution nonlinearity (i partial derivative(t)u - (-Delta)(alpha/2)u +/- (K * vertical bar u vertical bar(2))u = 0) with Cauchy data in the modulation spaces M-p.q(R-d). For K(x) = vertical bar x vertical bar(-gamma) (0 < gamma < min{alpha,d/2}) we establish global well-posedness results in M-p.q(R-d)(1 <= p <= 2, 1 <= q < 2d/(d + y)) when alpha = 2, d >= 1, and with radial Cauchy data when d >= 2, 2d/2d-1 < alpha < 2. Similar results are proven in Fourier algebra FL1 (R-d) boolean AND L-2(R-d). (C) 2019 Elsevier Inc. All rights reserved.