Function spaces related to continuous negative definite functions: ψ-Bessel potential spaces

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Levy processes and Fourier multipliers (2006, unknown): “results for anisotropic Sobolev spaces as in [ 9, Section 2.3 ], [13, Section 3.1].”
Harmonic analysis of additive Lévy processes (2007, background): “Farkas, Walter, Niels Jacob, and René L. Schilling.”
The refined Sobolev scale, interpolation and elliptic problems (2012, unknown): “Schilling [27], W.”
Characterisations of function spaces of generalised smoothness (2006, methodology): “We have already mentioned in the Introduction as well as in Section 3.3 that in [FJS01a] and [ FJS01b ] Bessel potential spaces H ψ,s p (R n ) associated to a continuous negative definite function ψ : R n → R were introduced and studied in the context of constructing a Markov process starting in eve”