Transistor and Resistors
Given that R19 is so much smaller than R20 I'd say the main purpose of R19 is to limit the current into the base of the transistor. This of course needs to be done in all grounded-emitter configurations.

The forward volt-drop of B-E is about 0.7V and it's quite easy to destroy a BJT without this current limiter.

R20 is less obvious - some engineers will put a resistor here because they may feel it is needed but in a lot of cases it isn't. The argument for its inclusion is debatable. If the application of the circuit were better known it might be possible to explain this resistor a bit better.