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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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