I have a handler (subclass of RequestHandler) which handles GET, POST, PUT and DELETE requests. The class also has independent functions which operates on DB. I am writing unit test for the class, but I am not able to initialize the class since it requires 2 arguments. How can I do it? 
Note: I don't have issues while testing rest calls.
The two arguments are the tornado.web.Application and the tornado.httputil.HTTPServerRequest. Normally, rather than constructing a RequestHandler directly, Tornado applications are tested via tornado.testing.AsyncHTTPTestCase which will create the handlers as needed. (You could construct the application and request by hand, but I wouldn't recommend it)
Do the functions you want to test need the application or request objects? If not, you could move them out of the subclass of RequestHandler to test them in isolation. If they do need either of these objects, then AsyncHTTPTestCase is the simplest way to get them.
Python - Tornado - How to write unit test for independent functions?