If you want to get last week publications you can do somehting like:
&fq=published_date:[NOW-7DAY/DAY TO NOW]
But if you want a concrete date you must do it in the SOLR date format:
&fq=published_date:[2013-07-17T00:00:00Z TO NOW]
Last but not least.
- use
[ ]for inclusive ranges - use
{ }for exclusive ranges - you can mix them like
[ }for inclusive – exclusive and vice versa{ ]
I hope that helps