Boundedness properties for pseudodifferential operators with symbols in the bilinear Hörmander 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.
Indiana University Mathematics Journal
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Published by the Indiana University Mathematics Journal, 2013
Link to publisher version of article: http://www.iumj.indiana.edu/IUMJ/FULLTEXT/2013/62/5168
Arpad Benyi, Frederic Bernicot, Diego Maldonado, Virginia Naibo, Rodolfo H.Torres, On the Hormander classes of bilinear pseudodifferential operators II, Indiana Univ. Math. J. 62 (2013), 1733-1764