Tohoku Mathematical Journal
2003
March
SECOND SERIES VOL. 55, NO. 1

Tohoku Math. J.
55 (2003), 131-140

Title FUNCTION SPACES AND CLASSES OF PSEUDODIFFERENTIAL OPERATORS

Author Wojciech Czaja and Ziemowit Rzeszotnik

(Received March 19, 2001)
Abstract. We introduce a new class of selfadjoint compact pseudodifferential operators, which is analogous to a class of elliptic unbounded pseudodifferential operators and is, therefore, suitable for obtaining upper and lower estimates on the eigenvalues of operators in this class. We prove such estimates and, as an application, we show that any operator from this class belongs to the Schatten-von Neuman class if and only if its symbol belongs to the Lorentz space.

2000 Mathematics Subject Classification. Primary 47G30.
Key words and phrases. Lorentz space, pseudodifferential operators, Schatten class, spectral asymptotics.

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