The open sleeve that AB8WH is referencing is several very closely
spaced elements of various lengths around a central element that is
directly driven by the feedline.

The other elements are very tightly coupled to the driven one because
they're so close, and so it's a good construction for broadening SWR
bandwidth (several overlapping resonances, elements almost the same
length) or making a multi band antenna (several widely spaced
resonances, elements widely different lengths)

- - - - - -

I think some HF multiband yagi manufacturers are using them... I don't
remember who. Also, many of the wideband long boom VHF yagi designs
have a director that ends up very closely spaced to the driven element,
essentially an open sleeve...

As to why you don't see more of them? I dunno, there are lots of ways
to make a multiband antenna. You could do the same thing out of tubing
but do it fan-dipole style and connect them all together. You could
use traps and cut out the amount of tubing you need. As far as
broadbanding, you typically only need it on the lower bands (80/75m
comes to mind) and there you'd be talking the erection of two ~70 foot
elements instead of one just to broaden your SWR curve even though
running a 3:1 SWR on your line and using the tuner in the rig would add
negligble loss. Better to take the other 70 feet of aluminum and space
it a half wavelength away from the first and phase them into a
broadside/endfire array.

I think the dimensions are a bit critical like a parallel multiband
dipole can be... lots of interaction between the elements. I don't
think they've got much of a marketing advantage right now, either.
Otherwise "open sleeve" would be an oft-heard buzzword in antenna ads
something like "linear loaded" or "no lossy traps".

Certainly an antenna construction worth knowing about, though... I
thought about building one when I first saw it too. Also, I was
playing with the possibility of adding a 2m yagi to my 6m moxon
rectangle the driven element of which would be open sleeve coupled.
Haven't had much success getting good front to back on 2m in the model
though, so I haven't pursued it. That's not the fault of the open
sleeveness... I think I need to start with a known good yagi design
first.

73,
Dan