my $s = do {local $/=undef; <DATA>};
while( $s =~ s#<span style="([^"]+)">(?!.*?<span)(.*?)</span>#span2tag($1,$2)#sgei ){};

sub span2tag {
  my ($attr, $s) = @_;
  if ($attr =~ /bold/)      { $s = "<b>$s</b>"; }
  if ($attr =~ /italic/)    { $s = "<i>$s</i>"; }
  if ($attr =~ /underline/) { $s = "<u>$s</u>"; }

  return $s;
}

__DATA__
this <span style="font-style: italic; font-weight: bold;">is</span> some
this <span style="font-weight: bold;">is</span> some
<span style="font-weight: bold; text-decoration: underline;">test
  <span style="font-style: italic;">text</span>
  <span style="text-decoration: underline;">for</span> bolding</span>, underlining and italicizing