How do I determine if my contribution to an area of research merits publication? I am a new worker in real functions with little experience and few published papers but not in top journals.

I together with my two colleagues found a new characterization of a well-known class of functions (first Baire class). I am pretty sure this is new. However, we cannot decide the extent of its significance because we are unable to find a good application. But suffice it to say there are some old results in the area that admit a very straightforward proof using our characterization. For instance, functions with countable discontinuities can be shown to be of first Baire class using our characterization with a very easy proof.

My question, is this enough for publication? I am afraid to submit it and got a snobbish review. By the way, I am from a third-world country.
If you don't submit a paper, you're never going to find out it's publishable—unless someone beats you to it. Basically, if you and your colleagues believe you have a publishable advance, then write it up and submit it. 

On a related note: have you solicited feedback from colleagues in the field? Has it been presented at a conference somewhere? What have you heard and done to "talk the work up" with colleagues? Has anyone told you it is (or is not) publishable?