Exponential moments of first passage times and related quantities for L\'evy processes

For a L'evy process on the real line, we provide complete criteria for the finiteness of exponential moments of the first passage time into the interval $(r,\mathrm{\infty })$, the sojourn time in the interval $(-\mathrm{\infty },r]$, and the last exit time from $(-\mathrm{\infty },r]$. Moreover, whenever these quantities are finite, we derive their respective asymptotic behavior as $r\to \mathrm{\infty }$.