some profile informations like youtube link doesnt seem

Your reply to gregory24 isn’t really explicit enough I’m afraid..

The reason you can display a FontAwesome icon without the if statement is only because this html <span class="fa fa-youtube">...</span> is loaded into the DOM of you page meanwhile your $youtube_profile variable is likely containing some value but your statement is wrong.

this should work if $youtube_profile isn’t empty:

<?php  
$youtube_profile = get_the_author_meta( 'youtube_profile' );

if ( !empty($youtube_profile) || $youtube_profile != '' ) {
    echo '<span class="fa fa-youtube"><a href="'.esc_url($youtube_profile).'"></a</span> ';
}
?>

BUT..
you don’t need to check twice for the same thing:
!empty($youtube_profile) AND $youtube_profile != '' checks are the same

the most simple way would be to simply check it like this, no need of checking if not FALSE just check if TRUE

if ( $youtube_profile ) { ... }