As pointed out in my comment above, most of the details are wrong in your implementation above. Fortunately in Drupal 7, there are six theming functions for the pager:

    下面的hook 超越 可以看看 

• theme_pager()
• theme_pager_first()
• theme_pager_link()
• theme_pager_last()
• theme_pager_previous()
• theme_pager_next()

These should allow you to make most of the customizations that you need. There's a good stackexchange answer about how to override Drupal theme functions() that you can refer to for the details.

Finally, you mentioned that you want to override the pager just for one page. I still think this might be worth doing with CSS alone, but in case it's not, you may be able to just override parts of the $variables array in whichever preprocess function contains the pager (I don't know off the top of my head if it's preprocess_page or preprocess_node or if it's accessible from any of the preprocess functions at all).

This is my answer from a previous post.

If you implement theme_pager you'll be expected to create the entire pager render array from scratch using several theme function - theme_pager_first, theme_pager_previous, theme_pager_next and theme_pager_last. That seems like entirely too much work for adding one class.

Since theme_pager calls theme_item_list at the very end to build the final render array, you can use hook_preprocess_HOOK to modify the pager render array before drupal renders it into HTML.

function THEME_preprocess_item_list(&$vars) {
  // make sure we're dealing with a pager item list
  if (isset($vars['attributes']['class']) && in_array('pager', $vars['attributes']['class'])) {
    // make sure there are items
    if (count($vars['items'])) {
      $vars['items'][0]['class'][] = 'test';
    }
  }
}

Clear the cache after adding this hook.

UPDATE: find the first li.pager-item:

function THEME_preprocess_item_list(&$vars) {
  // make sure we're dealing with a pager item list
  if (isset($vars['attributes']['class']) && in_array('pager', $vars['attributes']['class'])) {
    // loop the items and find the first .pager-item
    foreach ($vars['items'] as $index => $item) {
      if (in_array('pager-item', $item['class'])) {
        $vars['items'][$index]['class'][] = 'test';
        break;
      }
    }
  }
}

UPDATE2: find first and last li.pager-item:

function azamara_preprocess_item_list(&$vars) {
  // make sure we're dealing with a pager item list
  if (isset($vars['attributes']['class']) && in_array('pager', $vars['attributes']['class'])) {

    // loop the items and find the first and last .pager-item
    $first = FALSE;
    $last = NULL;
    foreach ($vars['items'] as $index => $item) {
      if (in_array('pager-item', $item['class'])) {

        // first
        if (!$first) {
          $vars['items'][$index]['class'][] = 'test';
          $first = TRUE;
        }

        // last
        $last = $index;
      }
    }

    if (!empty($last)) {
      $vars['items'][$last]['class'][] = 'test2';
    }
  }
}