, Volume 13, Issue 2, pp 271-284

Boundedness and spectral invariance for standard pseudodifferential operators on anisotropically weighted LP-Sobolev spaces

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Abstract

It is shown that pseudodifferential operators with symbols in the standard classes S ρ,δ m (ℝn) define bounded maps between large classes of weighted LP-Sobolev spaces where the growth of the weight does not have to be isotropic. Moreover, the spectrum is independent of the choice of the space.

Dedicated to Professor Israel Gohberg on the occasion of his sixtieth birthday