Spectral invariance for pseudodifferential operators on weighted function spaces (Q1331743)

The authors consider pseudo-differential operators with symbol in the Hörmander class \(S^ 0_{1,\gamma}\), \(0\leq\gamma <1\). These operators are known to be continuous on spaces similar to the Triebel- Lizorkin and Besov spaces [cf. \textit{L. Paeivaerinta}, Z. Anal. Anwend. 2, 235-242 (1983; Zbl 0544.47046)]. The authors consider a weighted version of these spaces [cf. \textit{H.-J. Schmeisser} and \textit{H. Triebel}, Topics in Fourier analysis and function spaces (1987; Zbl 0661.46025)]\ and prove the spectral invariance on these weighted spaces of selfadjoint pseudo-differential operators.