On the Bilinear Hormander Classes in the Scales of Triebel-Lizorkin and Besov Spaces

摘要

Boundedness properties on the scales of inhomogeneous Triebel-Lizorkin and Besov spaces of positive smoothness are proved for pseudodifferential operators with symbols belonging to certain bilinear Hormander classes. These include classes of symbols of order zero for which the associated bilinear operators have Caldern-Zygmund kernels but are not necessarily bounded in the setting of Lebesgue spaces as well as classes that go beyond the Caldern-Zygmund theory. In addition, it is established that boundedness estimates on Lebesgue spaces for all operators with symbols in a given Hormander class imply Besov estimates for such operators. A related result is obtained for general bilinear multiplier operators.