is MacBook Air 2015 with 4gb ram compatible with Big Sur ?

Yes, but you must understand that there's a difference between "minimally compatible" and "performance compatible", between "can this be installed" and "will it make my MacBook Air run slower than it is now".

According to the site, yes, your MacBook Air is "compatible". You can check it and other years here: https://support.apple.com/en-us/HT201862

But 4 GB is not a lot of RAM. And on an older MacBook Air, especially if you have a smaller hard drive and are at 75%+ capacity, it may run slow.

The only way to find out is to try it or monitor the forums here for another user with an identical laptop who has tried it. But before you try it you should (obviously) backup your computer and be familiar with how to create a bootable flash drive with Mohave on it (and do so), in case you wish to return to Mohave (or Catalina or whatever you're using).

Information on how to create a bootable installer for MacOS Mohave is available in these forums as well as on Google. It's a good exercise to go through learning as having one on hand is smart to do.

Hope this helps.

My 2013 MBA with 4 gb is being killed with Big Sur and Safari is one of the worst memory offenders. I can have over a gig of free memory until I open Safari and watch the memory plummet. I've seen as low as 15 Mb after just a couple minutes of Safari usage. By contrast, I generally have 230 to 250 Mb while using Chrome but even that is way less than I had before updating to Big Sur.

According to Apple yes, it is. But I'm waiting for a couple of weeks before I try it on my MBA early 2015 4gb to see if any reports of disasters surface.

Yes.

How to upgrade to macOS Big Sur – Apple Support