The layout region panel extends from panel component. You can bind the 'onResize' event on a region panel. Please try this code:
<div class="easyui-layout" style="width:100%;height:350px;">
<div data-options="region:'west',split:true" title="West" style="width:100px;"></div>
<div data-options="region:'center',title:'Main Title',onResize:onResize">
</div>
</div>
<script type="text/javascript">
function onResize(width,height){
console.log(width)
}
</script>