Q: How to transfer purchased iPad applications to iPhone

Hi kjlapen,

Welcome to the Support Communities!  I would suggest you transfer your iPad purchases to your computer using iTunes.  Then connect your iPad to the computer and add the content that you want to your iPhone.  Not all iPad apps are compatible with iPhone, so check the compatibility in the app's information page.  

Re-download or transfer your iTunes Store purchases from an iPhone, iPad or iPod to a computer - Apple Support
http://support.apple.com/en-us/HT201267

If you have a question regarding whether you have the trial version or full version of an app, contact the iTunes Store Support team.

Apple - Support - Topic Selection

I hope this information helps ....

- Judy