Get Author Count By Day, Week and Month

I’m not where I can run the below, but potential typos, etc. aside, it should be able to point you in the right direction.

1) Limit Query

You could add Date Parameters to your query arguments to limit them.

$today = getdate();
$args = array(
    'date_query' => array(
        array(
            'year'  => $today['year'],
            'month' => $today['mon'],
            'day'   => $today['mday'],
        ),
    ),
    'posts_per_page' => -1,
);
$query = new WP_Query( $args );
$posts = $query->posts;

---

2) Build author_id => post count array

Then get all the author ids as array keys to force unique entries, and count as value:

$authors = array();
foreach( $posts as $post ) {
   if ( array_key_exists( $post->post_author ) {
        $authors[$post->post_author] = ++$authors[$post->post_author];
   }
   else {
        $authors[$post->post_author] = 1; 
   } 
}

---

3) echo author name and count

Then loop through that array to get the values:

foreach ( $authors as $author ) {

   // since the key is the numeric id, we will use it to get display name
   echo get_the_author_meta( 'display_name', key($author) ) .': '. $author;
}