directing non-www to www domains in multisite

Used the domain mapping plugin to map my subsite domains and it worked perfectly. But the resulting sites are non-www and I'd like to redirect them to www.

I tried

RewriteEngine On
RewriteCond %{HTTP_HOST} ^
RewriteRule (.*)$1 [R=301,L]

for one of the domains, but I got "this page isn't redirecting properly".

My current .htaccess looks like this:

RewriteEngine On
RewriteBase /
RewriteRule ^index\.php$ - [L]

# uploaded files
RewriteRule ^([_0-9a-zA-Z-]+/)?files/(.+) wp-includes/ms-files.php?file=$2 [L]

# add a trailing slash to /wp-admin
RewriteRule ^([_0-9a-zA-Z-]+/)?wp-admin$ $1wp-admin/ [R=301,L]

RewriteCond %{REQUEST_FILENAME} -f [OR]
RewriteCond %{REQUEST_FILENAME} -d
RewriteRule ^ - [L]
RewriteRule  ^[_0-9a-zA-Z-]+/(wp-(content|admin|includes).*) $1 [L]
RewriteRule  ^[_0-9a-zA-Z-]+/(.*\.php)$ $1 [L]
RewriteRule . index.php [L]

AddType text/x-component .htc

The first part is because the main site was originally an html site. I tried putting the subsite redirect after that part and then before that part and neither worked.

Any ideas?