Use a regex to see if the string contains only spaces (or whitespace, which also includes [ \t\r\f\n]):

    print "Spaces only\n"         if $var =~ /^ +\z/;
    print "Only whitespace\n"     if $var =~ /^\s+$/;
    print "Whitespace or empty\n" if $var =~ /^\s*$/;
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I used \z as the end of string anchor on the first one because you didn't specify whether the string was a line and a \n at the end might not be acceptable.