Let X1 and Y1 be two random variables. We have Cov(X1,Y1) = 0. Does this extend to any transformation X2 = g(X1) and Y2 = g(Y1), such that Cov(X2,Y2)? Here, g is a continuous function. For example, if we set X2 = X1^2 and Y2 = Y1^2. Do we then from Cov(X1,Y1) = 0 that Cov(X1^2,Y1^2) = 0?