Video website on google application engine
As Nick pointed out, it can be done and it won't be a straight forward implementation.
I would suggest using the Amazon EC2 service for video conversion and Amazon S3 for storing of videos while using App Engine for creating a fast reliable and unbelievably scalable front-end.
I am going to work on a video website where users/admin will be able to upload the videos and play them using some opensource javascript player. However, I want to know if it is a good idea to start this kind of project on google app engine considering its limitations to server and store the data. 
What are the issues which I may have to encounter on Google application engine and if there are any possible solutions for those issues.
Currently, I have doubts on converting the videos while uploading, creating images from the videos uploaded (something like ffmpeg for google app engine) and whether google app engine will allow streaming for large videos considering its request and response constraints.
Please suggest.
Thanks in advance.