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.
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Partial support by NSF under Grant DMS 1101327 is acknowledged.
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Communicated by Loukas Grafakos.
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Naibo, V. On the Bilinear Hörmander Classes in the Scales of Triebel-Lizorkin and Besov Spaces. J Fourier Anal Appl 21, 1077–1104 (2015). https://doi.org/10.1007/s00041-015-9398-x
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DOI: https://doi.org/10.1007/s00041-015-9398-x