Quick sort implementation in JavaScript in prototype style
Looks okay to me.


I would probably go for if ( i != j ) { which could be faster than if ( i &lt; j ) {
You have a ton of short variable names, I guess that's ok for a sorting routine, though I would still rename x to m(iddle).
I would have declared tempItem right under i and j


For the part you are not so interested in;


Capital S in Sort is reserved for constructors
I think reduce is more appropriate than forEach in DumpArray
You should not put code on the same line after an else statement
Now that I think about it the dump routine could be reduced to

Sort.prototype.DumpArray = function() {

var prefix = 'The content of array: [ ';
//Duck typing, just test for join
if( this.arrayTest.join )
    console.log( prefix + this.arrayTest.join(', ') + ' ]'  )
else
    console.log( "Input: " , this.arrayTest );
};