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Full-Text Articles in Physical Sciences and Mathematics
On The Hörmander Classes Of Bilinear Pseudodifferential Operators, Ii, Árpád Bényi, Frederic Bernicot, Diego Maldonado, Rodolfo H. (Rodolfo Humberto) Torres, Virginia Naibo
On The Hörmander Classes Of Bilinear Pseudodifferential Operators, Ii, Árpád Bényi, Frederic Bernicot, Diego Maldonado, Rodolfo H. (Rodolfo Humberto) Torres, Virginia Naibo
Mathematics Faculty Publications
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.