We discuss the behavior of various observables that depend on matrix elements of operators in the superconducting state within the model of hole superconductivity. In this model, the gap exhibits a linear dependence on the band energy, and the bandwidth depends on the carrier concentration and can become very small for low hole density. We study, in particular, the behavior of ultrasonic attenuation, NMR relaxation rate, and electromagnetic absorption, and present results for parameters expected to be in the range that describes the high-Tc oxides. It is found that the energy dependence of the gap does not give rise to qualitatively different behavior, but significant differences from weak-coupling BCS behavior occur at low hole concentration due to the extreme narrowness of the band.