star trek - Were the Dominion aware of the Borg?

Are there any canon sources which indicate that the Dominion was aware of the Borg? If so, do those sources indicate what the Dominion planned to do about them?

I find it hard to believe that they didn't know about the Borg, yet I don't recall seeing anything in any of the TV series or movies about what the Dominion might do about the Borg.

On a side note, it seems to me that the non-Borg races of all quadrants would have been done well to band together to take down the Borg.

Answer

In DS9 itself, the Borg were never involved in the plot. (After the first five minutes, which were a flashback to off-screen events during The Best of Both Worlds, Part 2. Here’s a decent list of Borg mentions in DS9.)

As such, the Dominion’s relationship to them was never explored. They do occupy very distant regions of space, so until the Founders reached the Alpha Quadrant via the wormhole, it’s conceivable that they just never encountered them (although, as @NateWatson notes in his answer — which is good, go vote it up! — apparently the Borg did have some sort of facility in the Gamma Quadrant).

Once the Founders did reach the Alpha Quadrant, they seemed to be fully occupied with manipulating and fighting the majors powers there, rather than worrying about a distant enemy of those powers who had only made two significant incursions into the region, on both occasions with a single ship that was destroyed.

(Out-of-universe, DS9 left the Borg to TNG and Voyager; presumably the writers felt it would do better if it had its own identity as a show, with its own villains. Ronald D. Moore confirmed, but did not explain, that decision in a web chat.)

There is another question that asks about assimilated Founders, and the answer describes a DS9 novel where a Founder discusses a failed Borg attempt to assimilate it.

That suggests that the Borg might not have been much of a threat to the Founders themselves. In DS9, the Founders wanted to impose order across then galaxy, seemingly to pre-emptively defend against mistreatment from “solids”. It’s possible that they wouldn’t mind much if the Borg assimilated everyone else; it’s less work for them to do.

(Although, as mg30rg comments, that doesn’t mean the Borg couldn’t or wouldn’t have killed Founders if they’d encountered them; just that they might not have been able to assimilate them.)