How important is it for the corresponding author to be known in the field he/she is going to publish? How important is it for the corresponding author to be known in the field he/she is going to publish? Is the academic position of the corresponding author influential? How about the co-authors?
Getting a paper accepted for publication in a normal journal is a matter of credibility: you must be able to convince the peer reviewers that the content of your paper is both true and novel.  Very high status journals such as Nature or Science work somewhat differently: there you cannot reach the peer reviewers until you first convince the editor that your work is "important" and "broadly interesting" enough to consider, which is a somewhat arbitrary process.  

Let us consider only normal journals, however, where the bulk of all publication takes place: they still have an editorial filter, but it is generally only to ensure a submission is at least vaguely on-topic, not plagiarized, and basically sane.  These are pretty low bars to pass, though they are definitely affected by being known.  If I see a paper that has come out with a well-known PI as author and that looks like a logical extension on their prior work, I'm unlikely to scrutinize carefully for being on-topic or sanity: it would be such a blow to the reputation of the PI to misbehave there that I am comfortable to take the small risk that the reviewers might get annoyed because the paper turns out to actually be crazy or off-topic.  Not being known won't generally hurt an author here, it will just mean their paper is more likely to actually get checked for topic and sanity, rather than simply trusted.

The peer reviewers are another matter.  Peer review is a very noisy process, and even when double-blinding is used, it is often possible to have a good idea when a well-known person is involved based on the methods that they are using.  Most peer reviewers are conscientious and try to do a good and neutral job, but a (frustrating) minority are sloppy, selfish, pushing an agenda, or abusive.  Even for those who are trying to do a good job are human and thus are subject to same standard cognitive flaws we all are, like implicit bias.  

All of this means that an unknown's credibility will likely be assessed differently than a person who is well-known as a good and careful researcher. The unknown person will generally either have to present stronger evidence to be believed or will have the evidence that they do present scrutinized more carefully.  That unknown will actually be better off, though, than a well-known person who has a history of sloppy or controversial work, who will typically have an even harder time convincing peer reviewers.

Do not draw the wrong lesson from this, however: a person most certainly can publish well as an unknown, early in their career, without relying on the name recognition of co-authors.  Many of us do exactly that.  It's just going to be somewhat harder than after one has already established a reputation as a careful and productive researcher.

Final note: if you ever find yourself saying "They only rejected my paper because I'm not [well-known / popular / one of the cool kids / etc]" then you are probably wrong and engaging in sour grapes kvetching.  If they rejected your paper, then you should also have been provided with clear information about what types of evidence would improve your ability to get accepted.  Do that instead.