I know about the class AB current amplifier (output voltage is same as input, but maximum possible output current is increased). You just use a circuit like shown here:

I also already know about the class A voltage amplifier (output voltage is higher than the input, but the maximum possible current is less) like shown in the picture below:

The advantage of class A is that it increases the voltage of the signal.
The disadvantage of class A is that is that it uses 0 volts (ground) as the lower voltage rail. This means that the input and the output must be capacitively coupled, and thus you lose any DC component in the input signal that you want to keep in the output.
The advantage of a class AB amplifier is that it can use a negative voltage for the lower voltage rail, thus keeping the voltage at the input port and output port at 0 volts. This means that the capacitive coupling on the input and output is unnecessary.
The disadvantage is that it is not a voltage amplifier. At most, the output voltage is equal to the input voltage.
What I need is an amplifier that has the positive and negative voltage rails like in a class AB amplifier, but that performs voltage amplification like a class A amplifier.
An op-amp might seem like the solution, but if you look at the specs of any op-amp, you will find its amplifying properties suffer at higher frequencies, and they go away completely at about 20khz (open loop gain of 1x at 20khz, and continues to decrease even further above 20khz). This is completely useless for an RF amplifier.
For an RF amplifier, you need an open loop gain of at least 100x at frequencies of at least 1 MHz (and that just gets you to the middle of the AM radio broadcast band). I've heard that to get this kind of gain, at these frequencies, you need to build your own amplifier with discrete transistors. op-amps just won't work. And, if you want to keep the DC component (for example in an oscilloscope with DC coupling), it will need to be based on the class AB amplifier (power supply has +volts to -volts, not +volts to 0volts), so that the input and output ports with nothing connected will be at 0 volts without the use of an AC coupling capacitor.
Can you post a schematic for a simple 2-transistor amplifier powered with + and - voltage supplies, who's output signal has a voltage (not current) gain?