ON THE CONSTANTS IN THE CORONA THEOREM AND THE IDEALS OF H-INFINITY

We use the 5-method to show th, corona solutions in the corona theorem can be taken at the order of c/delta2 log 1/delta as delta --> 0. Using the similar method, we also show that if \g(z)\ less-than-or-equal-to c(\f1(z)\2 + \f2(z)\2) 1/\log3/2+epsilon(\f1(z)\2+\f2(z)\2), for all z is-an-element-of D, then g is in the ideal I(f1, f2); generated by f2 and f2.