  It is well known that the Stein-Tomas $L^2$ Fourier restriction theorem can
be used to derive sharp $L^p$ bounds for radial Fourier multipliers such as the
Bochner-Riesz means. In a similar manner, $L^p \to L^2$ estimates for spectral
projection operators have been utilized in order to obtain sharp $L^p$ bounds
for spectral multipliers of self-adjoint elliptic pseudo-differential operators
on compact manifolds. In this paper, we refine an endpoint result for spectral
multipliers due to Seeger, providing endpoint bounds in terms of Besov spaces.
Our proof is based on the ideas from the recent work by Heo, Nazarov and
Seeger, and Lee, Rogers and Seeger on radial Fourier multipliers.
