On the Hörmander Classes of Bilinear Pseudodifferential Operators

By 'Arp'ad B'enyi, Diego Maldonado, V. Naibo, Rodolfo H. Torres. 2009

100 citations recorded by the source corpus.

Bilinear pseudodifferential operators with symbols in the bilinear analog of all the Hörmander classes are considered and the possibility of a symbolic calculus for the transposes of the operators in such classes is investigated. Precise results about which classes are closed under transposition and can be characterized in terms of asymptotic expansions are presented. This work extends the results for more limited classes studied before in the literature and, hence, allows the use of the symbolic calculus (when it exists) as an alternative way to recover the boundedness on products of Lebesgue spaces for the classes that yield operators with bilinear Calderón–Zygmund kernels. Some boundedness properties for other classes with estimates in the form of Leibniz’ rule are presented as well.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/94db3fc7675cb033bd361ecad3592ce43c79e41c

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Jarod Hart
2. Xinfeng Wu
3. Rodolfo H. Torres
4. Loukas Grafakos
5. Dachun Yang
6. Kabe Moen
7. 'Arp'ad B'enyi
8. Long Huang

In Mathematical Physics

1. Rodolfo H. Torres
2. Jarod Hart
3. Xinfeng Wu
4. Dachun Yang
5. Loukas Grafakos
6. Long Huang

Citations in the corpus

• Smoothing properties of bilinear operators and Leibniz-type rules in Lebesgue and mixed Lebesgue spaces (2017, result): “Similar estimates for more general classes of symbols were given by Bényi et al [8] and [9] and Naibo [52].”