Twitter's Advanced Search lets you construct the query you desire. Unfortunately, search results only seem to be for tweets posted within the past 24 hours or so right now; might just be a temporary limitation, not sure.
In any case, your request URL might look something like this (note the JSON and Atom types):
http://search.twitter.com/search?q=%23HASHTAG+from:USERNAME
http://search.twitter.com/search.json?q=%23HASHTAG+from:USERNAME
http://search.twitter.com/search.atom?q=%23HASHTAG+from:USERNAME
But with the current timeframe limitation, it's not very practical.