Error with search and missing www

When I try to search using mod_cpsearch, the resulting url ist missing www.
This means that the end-users get an error.

example: url ist www.domain.com/index.php

in the search result i see domain.com/index.php?option=com_custompr...&submit_search=Suche

and this is not displayed.

I'm positive Module cpsearch and CP component don't use any url-chopping function. Instead they rely on Joomla's ubiquitous JURI::Base() to gather the server url.
In your place I'd double check SEF setting and - above all - mod_rewrite directives in .htaccess file.