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No abstract uploaded!

No abstract uploaded!

Averages over smooth measures on smooth compact hypersurfaces in$R$^{$n$}are studied. With assumptions on the decay of the Fourier transform of the measure we obtain mixed norm estimates for these means, for example$L$^{$p$}estimates of multiparameter maximal functions over compact hypersurfaces.

We prove uniform local energy decay estimates of solutions to the wave equation on unbounded Riemannian manifolds with nontrapping metrics. These estimates are derived from the properties of the resolvent at high frequency. Applications to a class of asymptotically Euclidean manifolds as well as to perturbations by non-negative long-range potentials are given.