After spending lot of time in altering DNS entries finally managed to get my site running in Google app engine as sub domain 

UserAppId.appspot.com  as www.UserAppId.mydomain.com

************How To MAKE WORK with WWW *************

http://mydomain.com OR  http://www.mydomain.com

OK. How do I get  my domain directly by www and not as sub-domain???

Here is the answer!!!!!!

Add sub-domain pointing to your google app for e.g., userAppId.mydomain.com. The way for you is to get your top level domain linked to your google app i.e., is to realize that www is a sub-domain 

Step by step to set up

1. Click here to go to   http://appengine.google.com ( and sign in if you’re not already logged in )
2. Pick your google app id under ‘My applications‘
3. Go to  Application Settings in the left menu> Click on Add Domain under ‘Domain setup’ and then follow steps to link your domain with google app  [ Ignore this step if you've already linked your google app with your domain name ]
4. Click here to go to www.google.com/a/  and log in
5. go to Dashboard -> Scroll down to end of the page and select your google app under Google App engine section
6. userAppId settings page > choose Web address > click on Add new URL
7. Input www and then click on Add button
8. Using your domain hosting provider’s web interface, add a CNAME for www for your domain and point to ghs.google.com

Now you have www.mydomain.com linked to your app.