Can nuclear fusion occur in the atmosphere of hot jupiters?

I know Jupiter would crush us to an oblivion the further you go in to The planet as they found out with a satellite. But whether it would be enough to cause nuclear fusion I wouldn't of thought so no. The mass of star is so much more than Jupiter

Nope. A "hot" Jupiter is a gas giant that is hot because it is very close to its star. That heat from the proximity to the star could never be enough to result in fusion if that's what you're asking. Large brown dwarfs though, yes they can have limited fusion. Due to the same reasons as stars, not due to being close to a star....

Hot Jupiters? No, not massive enough. However there seems to be a continuum of sizes ranging from gas giants to stars. In the middle of the two extremes are the brown dwarves which look superficially like gas giant planets but they are large enough for deuterium fusion to occur but not full blown hydrogen fusion.

In full blown hydrogen fusion such as you would get in a star hydrogen is fused into deuterium then deuterium is fused into helium. In brown dwarf stars the process only goes half way hydrogen can be converted to deuterium but not to helium.

Hot Jupiters lack the requisite pressure at their cores (a million atmospheres is good enough), for which each needs to be at least 13 times (our) Jupiter's mass.

The pressure on Jupiter is far too low for fusion to happen

Not in the atmosphere...

You need a threshold amount of heat and pressure - which would only occur in the core of a mass by natural means.