  In this paper, we establish a generalized H{\"o}lder's or interpolation
inequality for weighted spaces in which the weights are non-necessarily
homogeneous. We apply it to the stabilization of some damped wave-like
evolution equations. This allows obtaining explicit decay rates for smooth
solutions for more general classes of damping operators. In particular, for
$1-d$ models, we can give an explicit decay estimate for pointwise damping
mechanisms supported on any strategic point.
