IUMJ

Title: On the Hormander classes of bilinear pseudodifferential operators II

Authors: Arpad Benyi, Frederic Bernicot, Diego Maldonado, Virginia Naibo and Rodolfo H. Torres

Issue: Volume 62 (2013), Issue 6, 1733-1764

Abstract:

Boundedness properties for pseudodifferential operators with symbols in the bilinear H\"ormander classes of sufficiently negative order are proved. The results are obtained in the scale of Lebesgue spaces, and in some cases, end-point estimates involving weak-type spaces and BMO are provided as well. From the Lebesgue space estimates, Sobolev ones are then easily obtained using functional calculus and interpolation. In addition, it is shown that, in contrast with the linear case, operators associated with symbols of order zero may fail to be bounded on products of Lebesgue spaces.