Integrability theorems with sign changing coefficients (Q1271931)

The author proves results concerning integrability theorems for power series with sign changing coefficients. The author improves results of \textit{P. Heywood} [J. Lond. Math. Soc. 32, 22-27 (1957; Zbl 0077.06001)] and some of his own results and he generalizes results of \textit{S. M. Mazhar} [Real Anal. Exch. 20, No. 2, 726-735 (1995; Zbl 0836.26004)]. An important fact in these results is the quasi-subadditive property of the functions appearing in the assertions and assumptions. This paper summarizes all the recognitions made by researchers and presents a general assertion being applicable to sharpen some known results. The results proved in this paper will also be useful to extend some further results known for non-negative coefficients to sign changing coefficients. A great number of results proved on this line can be generalized to sign changing coefficients using the idea treated in this paper. Useful applications and remarks are also given.