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Hörmander’s famous Fourier multiplier theorem ensures the -boundedness of whenever for some , where we denote by the set of functions satisfying the Hörmander condition for derivatives. Spectral multiplier theorems are extensions of this result to more general operators and yield the -boundedness of provided for some sufficiently large. The harmonic oscillator shows that in general is not sufficient even if has a heat kernel satisfying gaussian estimates. In this paper,...
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