Infinite-energy solutions to energy-critical nonlinear Schrödinger equations in modulation spaces

We prove new well-posedness results for energy-critical nonlinear Schrödinger equations in modulation spaces, which are larger than the energy space. First, we remove the $\varepsilon$-derivative loss in $L^p$-smoothing estimates for the linear Schrödinger equation, if $p$ is larger than the Tomas-Stein exponent. Next, we show local well-posedness results for nonlinear Schrödinger equations in modulation spaces containing the scaling critical $L^2$-based Sobolev space. The proof is carried out via bilinear refinements and adapted function spaces.