|May 24, 2016
In this talk, we study pointwise decay estimates for Fourier transform of measures on fractal sets. The finiteness of the energy of a measure does not imply the pointwise decay while it depends on geometric structures of the support of the measure. For an example a measure on a Cantor set does not decay at infinity. As a related topic, we consider generalized Stein-Tomas theorem on submanifolds with non-integer dimension.