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A. G. Georgiadis and M. Nielsen. Pseudodifferential Operators on Spaces of Distributions Associated with Non-negative Self-Adjoint Operators. Journal of Fourier Analysis and Applications, 23(3):344–378, 2017.
We consider Hörmander type symbols on a family of spaces associated with non-negative self-adjoint operators, and we prove boundedness of the corresponding pseudodifferential operators on both classical and non-classical Besov and Triebel--Lizorkin spaces. Consequently, this also covers the case of Sobolev spaces. As an application, we obtain boundedness of spectral multipliers on the mentioned spaces.
@article{Georgiadis:2016ab, Abstract = {We consider H{\"o}rmander type symbols on a family of spaces associated with non-negative self-adjoint operators, and we prove boundedness of the corresponding pseudodifferential operators on both classical and non-classical Besov and Triebel--Lizorkin spaces. Consequently, this also covers the case of Sobolev spaces. As an application, we obtain boundedness of spectral multipliers on the mentioned spaces.}, Author = {Georgiadis, A. G. and Nielsen, M.}, Bib2Html_Dl_Pdf = {http://link.springer.com/article/10.1007/s00041-016-9472-z}, Bib2Html_Pubtype = {Journal Article}, Date-Added = {2016-08-29 08:32:37 +0000}, Date-Modified = {2019-03-04 15:22:32 +0100}, Issn = {1531-5851}, Journal = {Journal of Fourier Analysis and Applications}, Number = {3}, Pages = {344-378}, Title = {Pseudodifferential Operators on Spaces of Distributions Associated with Non-negative Self-Adjoint Operators}, Volume = {23}, Year = {2017}, Bdsk-Url-1 = {http://dx.doi.org/10.1007/s00041-016-9472-z}}
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