February Fourier Talks 2012

Pseudodifferential operators are generalizations of translation invariant operators that play an important role in partial differential equations. The Hörmander classes of (linear) pseudodifferential symbols are defined by imposing certain simple and useful conditions on the symbols that characterize such pseudodifferential operators. In this talk we consider the bilinear counterparts of the Hörmander classes and discuss some continuity results for the corresponding operators. As it turns out, bilinearization can produce some surprises. In order to point out how the bilinear versions might deviate from the linear ones, we take a closer look at the bilinear versions of two classical results from the linear theory due to Calderón-Vaillancourt and C. Fefferman, respectively.