Attached is a simulation of a basic similar circuit except this circuit is not self oscillating.
It is not intended to represent a real fluro inverter circuit but the power stage operating principal is the same.
R1 depicts (Not accurately modelled) a fluro tube.
The frequency here is 20khz supplied by the 2 phase oscillator V1/V2
The light blu trace is the power reference Vm provided by the 2 capacitors (nominal half supply volts)
Purple trace is the current thru R1 which is AC.
Red trace is power switching.
The Vm voltage is actually a result of the current thru each capacitor as the other end of R1 is alternately switched between +V & Gnd by the 2 transistors.
Back to the original circuit (& question):...
The nom. 300Vdc would be from bridge rectified mains(220V) & a filter cap.
Ci bleeds off a bit of the main tube current to heat the filaments, much less filament current once the tube has ionised.
L1,L2,L3 is a base drive transformer for the transistors with L1 & L3 windings 180 deg. phase so each transistor turns on alternately.
L4 smooths the tube current waveform edges (& the C1 & Ch capacitors smooth the top of the current waveform).
The capacitor to GND from the power switching node(Q1-E) supresses transistor turn off oscillations (visible in simulation) & smooths tube current waveform.
The circuit will start by the top transistors turning on (via bleed resistor) & producing current thru L2 winding & this in turn produces base voltage in both L1/L3 windings, turning off Q1 & turning on Q2 & now it will oscillate.
There is very little symmetry in the design of the 2 base drive circuits, this would likely be a result of design testing to optimise the performance.
Fahime, what is your prime need to understand this circuits operation, are you intending to make an electronic ballast for a mains operated fluro.
Fluro inverters that I have played with prototyped have been low voltage 12, 50v although I have tried to & repaired some mains fluro inverters.
ToniG.au