Approximating mixed Hölder functions using random samples

Suppose f:[0,1]2.. is a (c,.) -mixed Hölder function that we sample at l points X1,.,Xl chosen uniformly at random from the unit square. Let the location of these points and the function values f(X1),.,f(Xl) be given. If l.c1nlog2n, then we can compute an approximation f. .f.f..L2=.(n..log3/2n),with probability at least 1.n2.c1, where the implicit constant only depends on the constants c>0 and c1>0.