Discrete bilinear operators and commutators

Abstract

We discuss boundedness properties of certain classes of discrete bilinear operators that are similar to those of the continuous bilinear pseudodifferential operators with symbols in the Hörmander classes $B{S}_{1,0}^{\omega }$. In particular, we investigate their relation to discrete analogues of the bilinear Calderón-Zygmund singular integral operators and show compactness of their commutators.

14 pages. Minor revision. To appear in J. Geom. Anal