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Kansas State University
On an Endpoint Mapping Property for Certain Bilinear Pseudodifferential Operators
Mapping properties of bilinear pseudodifferential operators are motivated by some of their applications in topics of analysis and PDEs such as fractional Leibniz rules, paraproducts and commutators.
The main result to be discussed will be the boundedness from $L^\infty \times L^\infty$ into $BMO$ of bilinear pseudodifferential operators with symbols in a range of bilinear Hörmander classes of critical order. Such boundedness property is achieved by means of new continuity results for bilinear operators with symbols in certain classes and a new pointwise inequality relating bilinear operators and maximal functions. The role played by these estimates within the general theory will be addressed.
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