# Fourier transform of function times periodic function

Suppose I have a function of the type:

h(t) = g(t)f(t)

where g(t) is a periodic function. Are there any nice properties relating to the fourier transform of such a product?

Edit: If not then what about if g(t) is taken as the complex exponential?

$$h(t) \Leftrightarrow H(f)$$
$$h(t) e^{-2 \pi i f_0 t} \Leftrightarrow H(f - f_0)$$