The hose attached to this garden sprayer had failed last season, but the hose fitting had become one with the sprayer. Soaking it with penetrating oil for far longer than seemed necessary didn’t help, so I tried brute force:

After convincing myself that wasn’t going to work, I cut the fitting off and tried the old standby of collapsing the threaded shell inward with a small punch:

That didn’t work, either: the shell really had become one with the sprayer.
As it turned out, the plastic sprayer body had begun to crack in several high-stress locations and would shortly become Yet Another Project. I cut my losses and tossed the hose and the sprayer.