Oliver Dragičević
University of Ljubljana, Ljubljana, Slovenia

In a joint work with A. Carbonaro we applied the notion of $p$-ellipticity for a study of generalized Schrödinger operators with complex coefficients, for which we proved bilinear $L^p \times L^q \rightarrow L^1$ estimates with $p,q$ being conjugate exponents. Such inequalities admit applications to holomorphic functional calculus. We also discuss a similar result for yet more general operators, namely, those involving first-order perturbations. As shown recently by A. Poggio, this requires a suitable extension of $p$-ellipticity.