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Boundedness for pseudodifferential operators on multivariate α-modulation spaces

Lasse Borup Department of Mathematical Sciences, Aalborg University Morten Nielsen Department of Mathematics, Washington University

TBD mathscidoc:1701.333085

Arkiv for Matematik, 44, (2), 241-259, 2005.2
The α-modulation spaces$M$^{$s$,α}_{$p$,$q$}($R$^{$d$}), α∈[0,1], form a family of spaces that contain the Besov and modulation spaces as special cases. In this paper we prove that a pseudodifferential operator σ($x$,$D$) with symbol in the Hörmander class$S$^{$b$}_{ρ,0}extends to a bounded operator σ($x$,$D$):$M$^{$s$,α}_{$p$,$q$}($R$^{$d$})→$M$^{$s$-$b$,α}_{$p$,$q$}($R$^{$d$}) provided 0≤α≤ρ≤1, and 1<$p$,$q$<∞. The result extends the well-known result that pseudodifferential operators with symbol in the class$S$^{$b$}_{1,0}maps the Besov space$B$^{$s$}_{$p$,$q$}($R$^{$d$}) into$B$^{$s$-$b$}_{$p$,$q$}($R$^{$d$}).
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@inproceedings{lasse2005boundedness,
  title={Boundedness for pseudodifferential operators on multivariate α-modulation spaces},
  author={Lasse Borup, and Morten Nielsen},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203617516723894},
  booktitle={Arkiv for Matematik},
  volume={44},
  number={2},
  pages={241-259},
  year={2005},
}
Lasse Borup, and Morten Nielsen. Boundedness for pseudodifferential operators on multivariate α-modulation spaces. 2005. Vol. 44. In Arkiv for Matematik. pp.241-259. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203617516723894.
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