give_me_last_Sunday('20110517') is 20110515
give_me_last_Sunday('20110604') is 20110529

function lastSunday(d) {
  var d = d.replace(/(^d{4})(d{2})(d{2}$)/,'$1/$2/$3');
  d = new Date(d);
  d.setDate(d.getDate() - d.getDay());
  return d;
}

<script type="text/javascript">
var myDate=new Date();
myDate.setFullYear(2011,4,16)

var a = myDate.getDate();
var t = myDate.getDay();
var r = a - t;
document.write("The date last Sunday was "  + r);

</script>

function lastSunday(d) {
  var d = d.replace(/(^d{4})(d{2})(d{2}$)/,'$1/$2/$3');

  d = new Date(d);
  d.setDate(d.getDate() - d.getDay());

  year = d.getFullYear()+'';
  month = d.getMonth()+1+'';
  day = d.getDate()+'';
  if ( month.length == 1 ) month = "0" + month; // Add leading zeros to month and date if required
  if ( day.length == 1 ) day = "0" + day;

  return year+month+day;
}