# Reference request - exponential decay with the Laplace transform

Let $$f \colon [0,\infty) \to [0,\infty)$$ be a continuous function and define its Laplace transform by $$\mathcal{L}f(\lambda) = \int_0^\infty f(t)e^{-\lambda t}\, dt, \quad \forall \lambda > 0.$$ Are there results giving sufficient conditions on $$\mathcal{L}f$$ which guarantee that $$f$$ decays exponentially fast at infinity? I am mainly looking for conditions on the regularity and/or decay of the Laplace transform. I am not at all familiar with this subject so any reference is greatly appreciated.