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A Hörmander-type spectral multiplier theorem for operators without heat kernel

Sönke Blunck (2003)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Hörmander’s famous Fourier multiplier theorem ensures the L p -boundedness of F ( - Δ D ) whenever F ( s ) for some s > D 2 , where we denote by ( s ) the set of functions satisfying the Hörmander condition for s derivatives. Spectral multiplier theorems are extensions of this result to more general operators A 0 and yield the L p -boundedness of F ( A ) provided F ( s ) for some s sufficiently large. The harmonic oscillator A = - Δ + x 2 shows that in general s > D 2 is not sufficient even if A has a heat kernel satisfying gaussian estimates. In this paper,...

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