Sampling frequency range of an discrete signal
In a simple word no. You can detect the presence of frequencies above the nyquist frequency but you can't categorically "know" what frequency they are. See this: -



This informs you that a sinewave at 0.6 x sampling frequency (or 1.2 x nyquist) can be appear as coming from frequencies of 0.4 Fs, 1.4 Fs or 1.6 Fs.

It's impossible to know which one is correct. Note also this can be extended to frequencies centred around 2.5, 3.5, 4.5 etc of Fs.

Also,exactly at Fs (or integer multiples of Fs) any signal present at those frequencies will be "detected" as zero or a DC level (phase angle dependent).

However it's not all bad news because even though you cannot "know" the frequency you can demodulate any movement on that "out-of-band-signal" and recover a modulating waveform intact. This is useful for software defined radios. It's called "under-sampling".