We study analytic smoothing effects for solutions to the Cauchy problem for the Schrödinger equation with interaction described by the integral of the intensity with respect to one direction in two space dimensions. The only assumption on the Cauchy data is the weight condition of exponential type and no regularity assumption is imposed.
"Analytic smoothing effect for solutions to Schrödinger equations with nonlinearity of integral type." Osaka J. Math. 42 (4) 737 - 750, December 2005.