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Journal of Fourier Analysis and Applications

, Volume 21, Issue 5, pp 1077–1104 | Cite as

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

  • Virginia Naibo
Article

Abstract

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 Hörmander classes. These include classes of symbols of order zero for which the associated bilinear operators have Calderón-Zygmund kernels but are not necessarily bounded in the setting of Lebesgue spaces as well as classes that go beyond the Calderón-Zygmund theory. In addition, it is established that boundedness estimates on Lebesgue spaces for all operators with symbols in a given Hörmander class imply Besov estimates for such operators. A related result is obtained for general bilinear multiplier operators.

Keywords

Bilinear pseudodifferential operators Hörmander classes  Triebel-Lizorkin and Besov spaces 

Mathematics Subject Classification

Primary: 35S0, 47G30 Secondary: 42B20, 42B35 

Notes

Acknowledgments

Partial support by NSF under Grant DMS 1101327 is acknowledged.

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Department of MathematicsKansas State UniversityManhattanUSA

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