New proof of the Hörmander multiplier theorem on compact manifolds without boundary

Xu, Xiangjin

doi:10.1090/S0002-9939-07-08687-X

New proof of the Hörmander multiplier theorem on compact manifolds without boundary
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Proc. Amer. Math. Soc. 135 (2007), 1585-1595 Request permission

Abstract:

On compact manifolds $(M, g)$ without boundary, the gradient estimates for unit band spectral projection operators $\chi _{\lambda }$ are proved for a second order elliptic differential operator $L$. A new proof of the Hörmander Multiplier Theorem (first proved by A. Seeger and C.D. Sogge in 1989) is given in this setting by using the gradient estimates and the Calderón-Zygmund argument.

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