system
Given the following post, respond as if you're commenting on Reddit:
human
[Dune] How did the Fremen successfully carry their jihad beyond Arrakis?

The Fremen are a relatively-small population of desert dwellers from a single planet, whose success in overthrowing the Padishah Emperor's forces was largely based on their skill in riding sandworms and the inability of the Sardaukar to use shields on Arrakis. They're not exactly well-placed to fight a galaxy-spanning campaign that "killed sixty-one billion, sterilized ninety planets, completely demoralized five hundred others [and] wiped out the followers of forty religions." (*Dune Messiah*). "Desert power" shouldn't count for much when you leave the desert behind.
gpt
The main thing is that after they control Arakis, they control the Spacing Guild.  That's your space superiority and air superiority right there.  Nobody moves without the Guild, and the Guild doesn't move without the Fremen.  

Also, with the Guild under your thumb, and no need to play by the rules of the Landsraad, there's nothing stopping you dropping atomics freely.  That's your sterilized planets explained, and a healthy chunk of the billions killed as well. 

The other bit is that riding worms isn't their main combat ability.  They're easily the equal or superior to the Sardaukar even without worms.  Desert power is one thing, but the Fremen are strong, fearless, highly motivated, and very resistant to logistical shortages.  They're just the best troops around.