Remarks on a result of Hardy

Abstract. We apply results on equivalent power series (see K.-H. Indlekofer [5]) to functions with given modulus of continuity and to functions holomorphic in \(\{z: |z|\leq1\}\setminus\{1\}\), and derive Hardy's theorem on the existence of power series which converge uniformly on the unit circle but not absolutely.

Key words and phrases. Conditionally convergent power series, conformally equivalent power series.