Subalgebras to a Wiener type algebra of pseudo-differential operators

@article{Toft2001,
abstract = {We study general continuity properties for an increasing family of Banach spaces $S^p_w$ of classes for pseudo-differential symbols, where $S^\infty _w=S_w$ was introduced by J. Sjöstrand in 1993. We prove that the operators in $\{\rm Op\}(S^p_w)$ are Schatten-von Neumann operators of order $p$ on $L^2$. We prove also that $\{\rm Op\}(S^p_w)\{\rm Op\}(S^r_w)\subset \{\rm Op\}(S^r_w)$ and $S^p_w\cdot S^q_w\subset S^r_w$, provided $1/p + 1/q =1/r$. If instead $1/p +1/q = 1+1/r$, then $S^p_ww * S^q_w\subset S^r_w$. By modifying the definition of the $S^p_w$-spaces, one also obtains symbol classes related to the $S(m,g)$ spaces.},
affiliation = {Blekinge Technical University, Department of Mathematics, IHN, 371-79 Karlskrona (Suède)},
author = {Toft, Joachim},
journal = {Annales de l’institut Fourier},
keywords = {pseudo-differential operators; Weyl calculus; Schatten-von Neumann classes; admissible functions; Hölder's inequality; Young's inequality; subalgebras; properties of pseudodifferential operators; symbols},
language = {eng},
number = {5},
pages = {1347-1383},
publisher = {Association des Annales de l'Institut Fourier},
title = {Subalgebras to a Wiener type algebra of pseudo-differential operators},
url = {http://eudml.org/doc/115950},
volume = {51},
year = {2001},
}

TY - JOUR
AU - Toft, Joachim
TI - Subalgebras to a Wiener type algebra of pseudo-differential operators
JO - Annales de l’institut Fourier
PY - 2001
PB - Association des Annales de l'Institut Fourier
VL - 51
IS - 5
SP - 1347
EP - 1383
AB - We study general continuity properties for an increasing family of Banach spaces $S^p_w$ of classes for pseudo-differential symbols, where $S^\infty _w=S_w$ was introduced by J. Sjöstrand in 1993. We prove that the operators in ${\rm Op}(S^p_w)$ are Schatten-von Neumann operators of order $p$ on $L^2$. We prove also that ${\rm Op}(S^p_w){\rm Op}(S^r_w)\subset {\rm Op}(S^r_w)$ and $S^p_w\cdot S^q_w\subset S^r_w$, provided $1/p + 1/q =1/r$. If instead $1/p +1/q = 1+1/r$, then $S^p_ww * S^q_w\subset S^r_w$. By modifying the definition of the $S^p_w$-spaces, one also obtains symbol classes related to the $S(m,g)$ spaces.
LA - eng
KW - pseudo-differential operators; Weyl calculus; Schatten-von Neumann classes; admissible functions; Hölder's inequality; Young's inequality; subalgebras; properties of pseudodifferential operators; symbols
UR - http://eudml.org/doc/115950
ER -