You could just do it iteratively instead of recursively (also assuming this goes in the one-time quick-n-dirty clean-up category) .. i.e. find all the inner <span ...>foo</span> instances (w/the help of a negative look-ahead--seeperlre) and replace them .. now repeat that until no more matches. 
my $s = do {local $/=undef; <DATA>};
while( $s =~ s#<span style="(font-weight: bold;|font-style: italic;|te
+xt-decoration: underline;)">(?!.*?<span)(.*?)</span>#span2tag($1,$2)#
+sgei ){};
print $s;

sub span2tag {
  my ($attr, $s) = @_;
  return "<b>$s</b>" if $attr =~ /bold/;
  return "<i>$s</i>" if $attr =~ /italic/;
  return "<u>$s</u>" if $attr =~ /underline/;
  return $s;
}
__DATA__
this <span style="font-weight: bold;">is</span> some
<span style="font-weight: bold;">test
  <span style="font-style: italic;">text</span>
  <span style="text-decoration: underline;">for</span> bolding</span>,
+ underlining and italicizing text.<br />

[download]
Update: Probably a little less efficient, but clearer code: 
my $s = do {local $/=undef; <DATA>};
while(1){
  my $matched = 0;
  $matched ||= $s =~ s#<span style="font-weight: bold;">(?!.*?<span)(.
+*?)</span>#<b>$1</b>#sgi;
  $matched ||= $s =~ s#<span style="font-style: italic;">(?!.*?<span)(
+.*?)</span>#<i>$1</i>#sgi;
  $matched ||= $s =~ s#<span style="text-decoration: underline;">(?!.*
+?<span)(.*?)</span>#<u>$1</u>#sgi;
  last unless $matched;
}

[download]

In reply to Re: Converting span tags. by davidrw
in thread Converting span tags. by the_0ne

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