On the Hormander classes of bilinear pseudodifferential operators II
Arpad BenyiFrederic BernicotDiego MaldonadoVirginia NaiboRodolfo Torres
35S0547G3042B1542B20Bilinear pseudodierential operatorsbilinear Hormander classessymbolic
calculusCalderon-Zygmund theory.
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.
Indiana University Mathematics Journal
2013
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10.1512/iumj.2013.62.5168
10.1512/iumj.2013.62.5168
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Indiana Univ. Math. J. 62 (2013) 1733 - 1764
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