Bilateral Laplace transform and existence of Fourier transform
The bilateral Laplace transform converges in a vertical strip $a&lt;\text{Re}\{p\}&lt;b$, called the region of convergence (ROC). Compare this to the bilateral $\mathcal{Z}$-transform which converges in an annulus centered at the origin of the complex plane: $r_1&lt;|z|&lt;r_2$. For causal signals we have $b=\infty$ and $r_2=\infty$.

If the vertical strip $a&lt;\text{Re}\{p\}&lt;b$ does not include the imaginary axis, i.e., if $0&lt;a&lt;b$ or $a&lt;b&lt;0$, the bilateral Laplace transform does not converge for $p=j\omega$ because the imaginary axis is not inside the ROC. Consequently, the Fourier transform does not exist because the corresponding integral does not converge. For the $\mathcal{Z}$-transform the analogous case would be that the ROC does not include the unit circle, in which case the discrete time Fourier transform does not exist.